Question

question 11 (5 points)

whats the equation of the parabola that has its vertex at \\((4,-1)\\) and a \\(y\\)-intercept at \\((0,7)\\)?

a) \\(y = \frac{1}{2}(x - 4)^2 + 1\\)

b) \\(y = \frac{1}{2}(x - 4)^2 - 1\\)

c) \\(y = -\frac{1}{2}(x + 4)^2 - 1\\)

d) \\(y = \frac{1}{2}(x + 4)^2 - 1\\)

Explanation:

Set up vertex form

Using the Parabola Vertex Form knowledge point

$$ y = a(x - h)^2 + k $$

$$
LATEXBLOCK0
$$

Solve for coefficient a

Using the Quadratic y-intercept knowledge point

$$
LATEXBLOCK1
$$

Write final equation

Using the Parabola Vertex Form knowledge point

$$ y = \frac{1}{2}(x - 4)^2 - 1 $$

Answer:

• A) \(y = 1/2(x - 4)^2 + 1\)
• B) \(y = 1/2(x - 4)^2 - 1\) (Correct answer)
• C) \(y = -1/2(x + 4)^2 - 1\)
• D) \(y = 1/2(x + 4)^2 - 1\)