In Exercises 1–4, the graph of a quadratic function is given. Write the function’s equation, selecting from the following options.
1.
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College Algebra Essentials
- Express the quadratic function f(x)=x2x6 in standard form, and sketch its graph.arrow_forwardRewrite the quadratic function in vertex form (which our OpenStax textbook also calls the standard form) and give the vertex. f(x) = [ 囡囡囡 Enter your answer as a point (a, b). Vertex: la f(x)=x²5xarrow_forwardlet g(x)=4x-2 g(a-5)arrow_forward
- Example 3: Given the function h(x) = (x-2)/(3x + 4) and g(x)= (x+5)/x, determine the point(s) of intersection.arrow_forwardPart A: f(a+h) Part B: f(a) Part C: f(a+h)-f(a) Part D: f(a+h)-f(a) all divided by harrow_forwardTo put the quadratic function f(x)=ax2+bx+c in standard form, we complete the ________________.arrow_forward
- The function f(x) = -(x + 3)² - 4 has a vertex of (-3, -4). %3D O True O Falsearrow_forwardIn Exercises 1-4, the graph of a quadratic function is given. Write the function's equation, selecting from the following options. f(x) = (x + 1) – 1 h(x) = (x – 1) + 1 g(x) = (x + 1)² + 1 j(x) = (x – 1)² – 1 %3D %3D %3D 1. y 2. 6 15- 6- 5+ 4- 3- 2- -4-3-2- i 23 4 3-2-1, i 2 3 4 -2- -2- 3. 4. 6- 5- 4- 4- 3. 3- 2- 1- -4-3-2-1 23 4 -4-3-2 i 2 3 4 -2- -2- 6n4 m Darrow_forwardThe function f(x) = x² + 8x+ 25 can be obtained from an even function g by shifting its graph horizontally and vertically. That even function is g(x) = Its graph has been shifted by to the left and up. Hint: Complete the Square.arrow_forward
- The graph of f(x)=-x-5x+6 has the point (1, 0) on it. True O Falsearrow_forwardThe gross domestic product (GDP; in trillions of dollars) for Country A and Country B can be approximated as follows where x=60 corresponds to the year 1960. Country A: f(x)=0.00013(1.103)x Country B: g(x)=0.0149(1.216)x The first full year in which Country A's GDP surpasses $27 trillion is ____arrow_forwarddescribes the height of the gymnast's feet above the ground, s(t), in feet, t seconds after dismounting. The graph of the function is shown, with unlabeled tick marks along the horizontal axis. Use the function to solve Exercises 65–66. s(t) 10 s(t) = -1612 + 8t + 8 8. 2 Time (seconds) 65. How long will it take the gymnast to reach the ground? Use this information to provide a number on each tick mark along the horizontal axis in the figure shown. 66. When will the gymnast be 8 feet above the ground? Identify the solution(s) as one or more points on the graph. Height (feet)arrow_forward
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