Question

1. find the key features of the function f(x), graphed here.

a. axis of symmetry:
b. vertex:
c. is the vertex a max or min?
d. x-intercepts (zeros):
e. y-intercept:

1. find the key features of the function f(x), graphed here.

a. axis of symmetry:
b. vertex:
c. is the vertex a max or min?
d. x-intercepts (zeros):
e. y-intercept:

Explanation:

Step1: Analyze first quadratic graph

Part a (Axis of Symmetry):

Identify vertical line through vertex.
The vertex of the first parabola is at $x=-2$, so axis of symmetry is $x=-2$.

Part b (Vertex):

Locate the peak of the downward parabola.
The vertex is $(-2, 1)$.

Part c (Max/Min):

Check parabola opens downward (peak = max).
The vertex is a maximum.

Part d (x-intercepts):

Find where graph crosses x-axis.
The graph crosses x-axis at $x=-3$ and $x=-1$, so intercepts are $(-3, 0)$ and $(-1, 0)$.

Part e (y-intercept):

Find where graph crosses y-axis.
The graph crosses y-axis at $(0, -3)$.

Step2: Analyze second quadratic graph

Part a (Axis of Symmetry):

Identify vertical line through vertex.
The vertex of the second parabola is at $x=-1$, so axis of symmetry is $x=-1$.

Part b (Vertex):

Locate the trough of the upward parabola.
The vertex is $(-1, -9)$.

Part c (Max/Min):

Check parabola opens upward (trough = min).
The vertex is a minimum.

Part d (x-intercepts):

Find where graph crosses x-axis.
The graph crosses x-axis at $x=-4$ and $x=2$, so intercepts are $(-4, 0)$ and $(2, 0)$.

Part e (y-intercept):

Find where graph crosses y-axis.
The graph crosses y-axis at $(0, -8)$.

Answer:

For Question 1:

a. $x=-2$
b. $(-2, 1)$
c. Maximum
d. $(-3, 0)$ and $(-1, 0)$
e. $(0, -3)$

For Question 2:

a. $x=-1$
b. $(-1, -9)$
c. Minimum
d. $(-4, 0)$ and $(2, 0)$
e. $(0, -8)$