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4) The graph of the quadratic function f(x) = (x-2)(x+8) intersects the y-axis (0, c). The vertex of the function is (-3,-12.5). The equation has two x values where f(x) = 12 and the first x value is at x = -10 a) Find the value of c. b) Write down the equation for the axis of symmetry of the graph. c) Write down the x-intercepts of the graph. d) Draw the graph of y = f(x) for -10 ≤ x ≤ 4 and -14 ≤ y ≤ 14

4) The graph of the quadratic function f(x) = (x-2)(x+8) intersects the y-axis (0, c). The vertex of the function is (-3,-12.5). The equation has two x values where f(x) = 12 and the first x value is at x = -10 a) Find the value of c. b) Write down the equation for the axis of symmetry of the graph. c) Write down the x-intercepts of the graph. d) Draw the graph of y = f(x) for -10 ≤ x ≤ 4 and -14 ≤ y ≤ 14

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The image contains the following mathematical problem related to the quadratic function: --- **Problem 4:** The graph of the quadratic function \( f(x) = \frac{1}{2}(x-2)(x+8) \) intersects the y-axis at \( (0, c) \). The vertex of the function is \( (-3, -12.5) \). The equation has two \( x \) values where \( f(x) = 12 \) and the first \( x \) value is at \( x = -10 \). **Tasks:** a) Find the value of \( c \). b) Write down the equation for the axis of symmetry of the graph. c) Write down the \( x \)-intercepts of the graph. d) Draw the graph of \( y = f(x) \) for \( -10 \leq x \leq 4 \) and \( -14 \leq y \leq 14 \). e) Use the symmetry of the graph to show that the second solution is \( x = 4 \). ---
Transcribed Image Text:The image contains the following mathematical problem related to the quadratic function: --- **Problem 4:** The graph of the quadratic function \( f(x) = \frac{1}{2}(x-2)(x+8) \) intersects the y-axis at \( (0, c) \). The vertex of the function is \( (-3, -12.5) \). The equation has two \( x \) values where \( f(x) = 12 \) and the first \( x \) value is at \( x = -10 \). **Tasks:** a) Find the value of \( c \). b) Write down the equation for the axis of symmetry of the graph. c) Write down the \( x \)-intercepts of the graph. d) Draw the graph of \( y = f(x) \) for \( -10 \leq x \leq 4 \) and \( -14 \leq y \leq 14 \). e) Use the symmetry of the graph to show that the second solution is \( x = 4 \). ---
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