Write the quadratic function y = x(x-4) - 6(x-4) in the following forms and state the values of all constants. (a) Standard form y y = a = b= C = a= (c) Vertex form y = a (x - h)² + k. y = h = = k= ax² +bx+c. (b) Factored Form y = a (x-r)(x - s). y = a = r || S=

f(x)=-4(x-2)^2-5 use the vertex and intercepts to sketch the graph of the quadratic function

Write the quadratic function in the standard form y = a(x - h)² + k. y = x² - 6x y = (x + 6)²-6 Oy = (x+3)²-3 Oy=(x-6)²-36 Oy=(x-3)²-9

Find a formula for the quadratic function with a vertex of (5,0) while f(6)=2

1. Write the quadratic function in standard form  f(x)=x^2-8x+21 =  2. Write the quadratic function in standard form and identify x intercepts with its smaller x and larger x value.  f(x)=-x^2-4x+1=  3. Write the quadratic function in standard form  f(x)=6x^2-x+1 4. Write the quadratic function in standard form  f(x)=-1/2x^2+4x-9

2 A golf ball is struck by a 60-degree golf club at an initial velocity of 90 feet per second. The height of the golf ball in feet is given by the quadratic function h(x) = 16x 77.9 + -x, where x is the 45 (45)² horizontal distance of the golf ball from the point of impact. What is the horizontal distance of the golf ball from the point of impact when the ball is at its maximum height? What is the maximum height obtained by the golf ball? The horizontal distance of the golf ball from the point of impact when the ball is at its maximum height is (Round to two decimal places as needed.) feet.

Identify the vertex, axis of symmetry, and x-intercept(s). vertex     (x, f(x)) =               axis of symmetry               x-intercept     (x, f(x)) =                (smaller x-value) x-intercept     (x, f(x)) =                (larger x-value)

Given the quadratic function f(x) = (x+2)^2-5 Find the y-intercept

The purpose of this analysis is to model available atmospheric carbon dioxide data with a quadratic function of the form f(x) = ax2 + bx + x.  In the space below, type the model quadratic function for the relationship between year and mean carbon dioxide levels in standard mathematical form using the coefficients calculated on the spreadsheet.          Using the model equation, determine the mean atmospheric carbon dioxide levels in the year 2030.             Using the model equation, determine the mean atmospheric carbon dioxide levels in the year 2050.             What other factors might need to be taken into account to provide a more robust model to make predictions              regarding future atmospheric carbon dioxide levels?