Question 5 The graph of the quadratic function f(x)=(æ – 2)(r + 8) intersects the y-axis at (0, c). The vertex of the function is (-3, – 12.5). The equation f(r)= 12 has two solutions. The first solution is a= -10. Let T be the tangent at z = -3. a. Find the value of c. b. Write down the equation for the axis of symmetry of the graph. c. Use the symmetry of the graph to show that the second solution is = 4.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.1: Quadratic Functions And Models
Problem 2E: The quadratic function f(x)=a(xh)2+k is in standard form. (a) The graph of f is a parabola with...
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The graph of the quadratic function f(x)=1/2(x-2)(x+8) intersects the y-axis at (0,c).

Question 5
The graph of the quadratic function f(z)= (x – 2)(x + 8) intersects the y-axis at (0, c).
The vertex of the function is (-3, – 12.5).
The equation f(x)= 12 has two solutions. The first solution is =
-10.
Let T be the tangent at z = -3.
a. Find the value of c.
b. Write down the equation for the axis of symmetry of the graph.
c. Use the symmetry of the graph to show that the second solution is æ = 4.
d. Write down the a-intercepts of the graph.
e. On graph paper, draw the graph of y = f(x) for -10 <a< 4 and -14 <y < 14. Use a scale of 1 cm to represent 1 unit on the z-axis and
1 cm to represent 2 units on the y-axis.
f.l. Write down the equation of T.
f.ii. Draw the tangent T on your graph.
g. Given f(a)= 5.5 and f'(a)= -6, state whether the function, f, is increasing or decreasing at z = a. Give a reason for your answer.
Transcribed Image Text:Question 5 The graph of the quadratic function f(z)= (x – 2)(x + 8) intersects the y-axis at (0, c). The vertex of the function is (-3, – 12.5). The equation f(x)= 12 has two solutions. The first solution is = -10. Let T be the tangent at z = -3. a. Find the value of c. b. Write down the equation for the axis of symmetry of the graph. c. Use the symmetry of the graph to show that the second solution is æ = 4. d. Write down the a-intercepts of the graph. e. On graph paper, draw the graph of y = f(x) for -10 <a< 4 and -14 <y < 14. Use a scale of 1 cm to represent 1 unit on the z-axis and 1 cm to represent 2 units on the y-axis. f.l. Write down the equation of T. f.ii. Draw the tangent T on your graph. g. Given f(a)= 5.5 and f'(a)= -6, state whether the function, f, is increasing or decreasing at z = a. Give a reason for your answer.
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