Question

question 13 (5 points)
whats the equation of the parabola that has its vertex at \\((8,-14)\\) and a point \\((5,13)\\) that lies on the curve?

a) \\(y = 3(x - 8)^2 - 14\\)

b) \\(y = 3(x + 8)^2 - 14\\)

c) \\(y = (x + 8)^2 - 14\\)

d) \\(y = (x - 8)^2 - 14\\)

Explanation:

Identify the vertex form of a parabola

Using the Parabola Vertex Form knowledge point

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

where the vertex is \((h, k) = (8, -14)\).

Substitute the vertex coordinates

Using the Parabola Vertex Form knowledge point

$$ y = a(x - 8)^2 - 14 $$

Substitute the given point to solve for a

Using the Parabola Vertex Form knowledge point

$$
LATEXBLOCK0
$$

Write the final quadratic equation

Using the Parabola Vertex Form knowledge point

$$ y = 3(x - 8)^2 - 14 $$

Answer:

• (A) \(y = 3(x - 8)^2 - 14\) (Correct answer)
• (B) \(y = 3(x + 8)^2 - 14\)
• (C) \(y = (x + 8)^2 - 14\)
• (D) \(y = (x - 8)^2 - 14\)