Question

question 6 (5 points)
consider the function \\(g(x) = x^2 + 6x + 5\\). now consider the quadratic function \\(h(x)\\), which has values given in the table of values below. which function has a greater y-intercept?

\\(\

$$\begin{array}{|c|c|c|c|c|c|}\\hline x & 0 & 1 & 2 & 3 & 4 \\\\ \\hline h(x) & 9 & 4 & 1 & 0 & 1 \\\\ \\hline\\end{array}$$

\\)

a) \\(g(x)\\) has a greater y-intercept.
b) neither function has a y-intercept.
c) \\(h(x)\\) has a greater y-intercept.
d) the y-intercepts of \\(g(x)\\) and \\(h(x)\\) are equal.

question 7 (5 points)
select the function that represents a parabola with vertex at \\((2,-1)\\) and a point \\((5,8)\\) on its curve.

a) \\(f(x) = (x-2)^2 - 1\\)
b) \\(f(x) = 2(x-2)^2 - 1\\)
c) \\(f(x) = (x+2)^2 - 1\\)
d) \\(f(x) = 2(x+2)^2 - 1\\)

Explanation:

Find the y-intercept of g(x)

To find the y-intercept of \(g(x) = x^2 + 6x + 5\), we evaluate the function at \(x = 0\):

$$ g(0) = 0^2 + 6(0) + 5 = 5 $$

Thus, the y-intercept of \(g(x)\) is \(5\).

Find the y-intercept of h(x)

The table provides values for \(h(x)\). The y-intercept occurs where \(x = 0\). Looking at the table:

• When \(x = 0\), \(h(0) = 9\).

Thus, the y-intercept of \(h(x)\) is \(9\).

Compare the y-intercepts

We compare the two y-intercept values:

• \(g(0) = 5\)
• \(h(0) = 9\)

Since \(9 > 5\), \(h(x)\) has a greater y-intercept. This corresponds to option C.

Determine the vertex form of the parabola

Using the Parabola Vertex Form knowledge point

$$
LATEXBLOCK0
$$

Solve for the leading coefficient a

Using the Parabola Vertex Form knowledge point

$$
LATEXBLOCK1
$$

This corresponds to option A.

Answer:

Question 6

• (A) \(g(x)\) has a greater y-intercept.
• (B) Neither function has a y-intercept.
• (C) \(h(x)\) has a greater y-intercept. (Correct answer)
• (D) The y-intercepts of \(g(x)\) and \(h(x)\) are equal.

Question 7

• (A) \(f(x) = (x - 2)^2 - 1\) (Correct answer)
• (B) \(f(x) = 2(x - 2)^2 - 1\)
• (C) \(f(x) = (x + 2)^2 - 1\)
• (D) \(f(x) = 2(x + 2)^2 - 1\)