Question

for the quadratic function f(x)=x²+2x-8, answer parts (a) through (c).
(a) is the graph concave up or concave down?
○ concave down
○ concave up
(b) find the y-intercept and the x-intercepts, if any.
what is the y-intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
○ a. the y-intercept is
(type an integer or a simplified fraction.)
○ b. there is no y-intercept.
what is the x-intercept? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
○ a. the x-intercept(s) is/are
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
○ b. there is/are no x-intercept(s).
(c) use parts (a) and (b) to graph the function.
use the graphing tool to graph the function.
this quiz: 25 points possible
this question: 1 point(s) possible

Explanation:

Part (a)

Step 1: Recall concavity rule for quadratic

For \( f(x) = ax^2 + bx + c \), if \( a > 0 \), concave up; \( a < 0 \), concave down.
Here, \( f(x) = x^2 + 2x - 8 \), so \( a = 1 > 0 \).

Part (b)

Step 1: Find y - intercept

Y - intercept is at \( x = 0 \). Substitute \( x = 0 \) into \( f(x) \): \( f(0)=0^2 + 2(0)-8=-8 \).

Step 2: Find x - intercepts

Set \( f(x)=0 \): \( x^2 + 2x - 8 = 0 \). Factor: \( (x + 4)(x - 2)=0 \). Solve: \( x=-4 \) or \( x = 2 \).

Answer:

s:
(a) Concave up
(b) Y - intercept: A. The y - intercept is \(-8\); X - intercepts: A. The x - intercept(s) are \(-4, 2\)
(c) (Graphing: Plot the y - intercept \((0, - 8)\), x - intercepts \((-4, 0)\) and \((2, 0)\). Since concave up, the parabola opens upward, passing through these points.)