Question

Which equation is equivalent to the formula: y=a(x−h)2+k?

A) ʸ⁼ᵃˣ²−²ᵃʰˣ⁺ᵃʰ²⁺ᵏʸ⁼ᵃˣ²−²ᵃʰˣ⁺ᵃʰ²⁺ᵏ
B) ʸ⁼ᵃˣ²−²ᵃʰˣ⁺ᵃʰ²−ᵏʸ⁼ᵃˣ²−²ᵃʰˣ⁺ᵃʰ²−ᵏ
C) ʸ⁼ᵃˣ²−²ᵃʰˣ⁺ᵃʰ²
D) ʏ=ᴀ(x−ʜ)2−ᴋ

Answer 1

The equivalent equation to y=a(x-h)^2+k is obtained by expanding the squared term and distributing the coefficient a. The matching equation is y=ax^2-2ahx+ah^2+k, which corresponds to Option A.

Step-by-step explanation:

The equation y=a(x-h)^2+k is a standard form equation of a parabola, where a affects the width and direction of the parabola, (h,k) is the vertex of the parabola, and x and y are the variables. To find an equivalent equation, we need to expand the given formula to make it look similar to the standard quadratic equation format, which is y=ax^2+bx+c.

Let's expand the given formula:

1. Square the binomial: y=a(x^2-2hx+h^2)+k
2. Distribute the a across the squared terms: y=ax^2-2ahx+ah^2+k

The equation that matches this format is Option A, which is y=ax^2-2ahx+ah^2+k. This is the expanded form of the given quadratic equation in vertex form.