If b2 - 4ac > 0, which of the following conclusions can be made about the graph of f(x) = ax2 + bx + c, a ≠ 0?(a) The graph has two distinct x-intercepts.(b) The graph has no x-intercepts.(c) The graph has three distinct x-intercepts.(d) The graph has one x-intercept.

Q: The function f(x) = kx* + 8x² has three turning points, a maximum value of 8 and a root at x = 2.…

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Q: how is the graph g(x)=(x-6)^2-4 related to the graph of f(x)=x^2?

A: In this question transfomation takes place.

Q: True or False If the discriminant b2 - 4ac = 0, the graphof f(x) = ax2 + bx + c, a ≠ 0, will touch…

A: Quadratic equations ax2 + bx + c = 0 ,a ≠ 0 discriminant D =  b2 - 4ac

Q: How Is the graph of g (x)=x2+14 related to the graph of f(x)=x2? The graph of g (x)=x²+14Is the…

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Q: what is the decreasing interval for the following function: y = -1/4x-5

A: The given function is: y=-14x-5 The function f(x) decreases when f'(x) < 0.

Q: Suppose that the​ x-intercepts of the graph of y=​f(x) are 2 and 9. ​(a) What are the​ x-intercepts…

A: Change  Coordinates change f(x) → f(x+h)  (x, y) → (x-h, y) f(x) → f(x-h)  (x, y) → (x+h, y)…

Q: neath the graph of f(x) = 7x³ about the y-axis ov

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Q: Suppose that f(x) = x2 + 4x - 21.(a) What is the vertex of f?(b) What are the x-intercepts of the…

A: a. The vertex parabola lies at x=-b2a for the f(x) =ax2+bx+c vertex is at x…

Q: Suppose that the x intercepts of the graph of y=f(x) are -5 and 3. What are the x intercepts of the…

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Q: If f(4) = – 2, then the point is on the graph - of f.

A: In the question we have to find point on graph.

Q: what is the end behavior of the graph f (x) = -0.5x^2 - 3x -4

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Q: The graph of g(x) = ax2 opens downward and is narrower than the graph of f(x) = x2  what is value a?

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Q: When g(x) is x+6/2 When f(0) is -3 What is g-1f(0)

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Q: snip

A: Given the function y=fx and its x-intercepts are -5 and 3 then factors of function would be -5 and 3…

Q: If h(x)=−8x^3−8x^2−8x−5, determine whether the graph of h(x) is concave up or down when x=3.

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Q: Suppose that the x-values of the x-intercepts of the graph of y = f(x) are -3 and 5. What are the…

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Q: Find an equation for the graph sketched belo 구 -5 4 -3 -2 -1 3 4 -2 -3 -4 -6 -7- -8+ f(x) =| 3. 2.

A: The solution is given below:

Q: The graph of f(x) = x³ + 6x² + 7x has a point of inflection at r = -5 -2 1 -1 O 3

A: Consider the following function: fx=x3+6x2+7x Differentiate fx with respect to x:…

Q: How does the graph of f(x)=(x-9)'-3 Compare to the parent function gx) = x". |

A: Given, f(x)=(x-9)4-3 g(x)=x4

Q: The graph of f(x) = x2 – 7 is horizontally stretched by a factor of 4.5. Write the equation…

A: Here the graph of f(x)=x²-7 is horizontally stretched by a factor of 4.5.  We want to write the…

Q: Suppose that f(x) = x2 + 2x - 8.(a) What is the vertex of f?(b) What are the x-intercepts of the…

A: (a) Given function is: fx=x2+2x-8 Let y = f(x) Then we get,…

Q: Suppose that the x-values of the x-intercepts of the graph of y = f(x) are -6 and 5. What are the…

A: Add 3 in the x, We get (x+3) Shift the graph to the left by 3 unit.

Q: 2. Graph the function: f(x) = S 3x 3x if x < -1 (2x +1 if -1 < x < 3 -2+ -3+ -5+ -6+ -7+ -8+ -9+

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Q: Suppose that the​ x-intercepts of the graph of y=​f(x) are −7 and −4.

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Q: Find the x-intercepts of the graph of f(x)= 4x2 + 8x - 3.

A: Given :            f(x) = 4x2 + 8x - 3

Q: The graph of g(x)=ax2g(x)=ax^2 opens downward and is narrower than the graph of f(x)=x2f(x)=x^2.…

A: Use the properties of leading coefficient of a polynomial and identify the value of a.

Q: Determine the points of intersection of the graphs of f(x) = x2 + 5x + 1 and g(x) = - 2x2 - 11x - 4…

A: To find the point of intersection, we need to equate both the functions to each other. Then after…

Q: . The x-coordinate of the vertex of f(x) = ax2 + bx + c,a ≠ 0, is_________

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Q: 11. Suppose that the x-intercepts of the graph of y = f (x) are –5 and 14. a) What are the…

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Q: How does the graph of f(x) = (x + 7)3 − 8 compare to the parent function g(x) = x3?

A: Givenf(x)=(x+1)3-8 g(x)=x3here,g(x) is the parent function and f(x) is its transformed function

Q: the graph of the quadratic function f(x) = x2 + dx + 5d has its vertex on the x-axis, what are the…

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Q: If f(x) = 3x^2 − 7 and g(x) = 2x + a, find a so that the graph off ◦ g crosses the y-axis at 68.

A: Given

Q: How would the graph of f(x) = ✔x be affected if it were changed to g(x) = -2✔x?

A: Because the 2 was multiplied with f(x), so f(x) will stretch vertically by a factor of 2.  Because…

Q: Suppose (7,-2) is a point on the graph of y=f(x). What is the point that will be on the graph of…

A: Solution is given below:

Q: The x-coordinate of the vertex of f(x) = ax2 + bx + c, a ≠ 0, is ________.

A: For the standard form of a parabola:  fx=ax2+bx+c If a&gt;0, the parabola opens up and the vertex…

Q: how can the graph of f(x)=1/(x-9)^2 + 7 be obtained from the graph of y= 1/x^2 ?

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Q: Find an equation for the graph sketched below: 8- 7- 2- -5 4 -3 -2 - i 2 3 4 5 -2- -7 -8- f(x) =

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Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = x3 −…

A: Consider the following function: fx=x3-9x2+24x-18 Differentiate fx with respect to x:…

Q: Suppose that the x-intercepts of the graph of y = f(x) are - 5 and 3.(a) What are the x-intercepts…

A: Given: x-intercepts of the graph  y=f(x) are -5 and 3

Q: 3. Sketch the graph of f(x) = 2x2 – 5x – 6. Find all intercepts and the vertex.. 10 x-intercepts: 8.…

A: To find x intercepts we set f(x)=0 and solve for x Answer: x-intercepts: 3.386 and -0.886

Q: If the graph of the quadratic function f(x) = x2 + 5dx + d2 + 1 has its vertex on the x-axis, what…

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Q: Determine the intercepts of the graph of f(x) = -4x - and 0, 16 (3,0) and 0, and 0, 16 0 and 0, 16 O…

A: Please refer the attached image for complete solution.THANK YOU.

Q: how is the graph of g(x)=x³+2 related to the graph of f(x)=x^3

A: The graph of  x3 and x3+2 are related to each other.  Both the graphs work in same sense but graph…

Q: The axis of symmetry of the graph of f(x) = −2x² − 4 is the line y = 0. - Select one: True False

A: Given that the axis of symmetry of the graph of fx=-2x2-4 is the line y=0.

Q: In the function:  f(x)= (7x+B)/(4x+b) , with 7b&gt;4B When is the function increasing and when is…

A: Function is increasing where slope f’(x) &gt;0 and decreasing where f’(x) &lt;0. Find the derivative…

Q: 2+7+12 Find the r-intercepts of the function f (x) = Enter your solution as a list of x-values,…

A: f(x)=x2+7x+12x2+6x-3For x-intercept, f(x)=0

Q: For any real x, what is the maximum value of the expression y = 2(k-x)(x+√x²+k²)?

A: This question can be solved using the concept of maximum and minimum.

Q: Suppose (1, 3) is a point on the graph of y = f(x).• What point is on the graph of y = f(x + 3) −…

A: y = f(x + 3) − 5 means y=f(x) moved 3 units left and 5 units down. (x,y) -&gt; (x-3 , y-5). So,…

Q: suppose that the x-intercepts of the graph of y=f(x) are: -7 and 2  what are the x-intercepts of the…

A: The x intercepts of the graph, y is given below.