Question

question 19 (5 points)
find the focus and the directrix of the parabola with the equation (y = \frac{1}{4}(x - 6)^2 + 5)

a) focus = ((-5, 6)), directrix is (y = -4)
b) focus = ((6, 6)), directrix is (y = 4)
c) focus = ((5, -6)), directrix is (y = -7)
d) focus = ((6, -6)), directrix is (y = -4)

question 20 (5 points)
select the function that represents a parabola with vertex at ((2, 1)) and y-intercept ((0, 3)).

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

Explanation:

Identify vertex and parameter p

Using the Parabola Focus and Directrix and Parabola Vertex Form knowledge points

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Calculate focus and directrix

Using the Parabola Focus and Directrix knowledge point

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Use vertex form for Question 20

Using the Parabola Vertex Form knowledge point

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Solve for vertical stretch factor

Using the Quadratic y-intercept and Parabola Vertex Form knowledge points

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Answer:

Question 19

• (A) Focus = (-5,6), directrix is y = -4
• (B) Focus = (6,6), directrix is y = 4 (Correct answer)
• (C) Focus = (5,-6), directrix is y = -7
• (D) Focus = (6,-6), directrix is y = -4

Question 20

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