Question

Given the vertex (4,-1) and a point of (5,2) that is passes through. What is the euation of the quadratic in vertex form.

A. y = (x - 4)^2 - 1
B. y = (x + 4)^2 - 1
C. y = (x - 4)^2 + 1
D. y = (x + 4)^2 + 1

Answer 1

The equation of the quadratic in vertex form is y = 3(x - 4)^2 - 1.

Step-by-step explanation:

The equation of the quadratic in vertex form can be determined using the given vertex and a point it passes through. The vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) is the vertex. To find the value of a, we can substitute the coordinates of the given point (5, 2) into the equation. We have:

y = a(x - 4)^2 - 1

Substituting the point (5, 2) into the equation:

2 = a(5 - 4)^2 - 1

2 = a(1)^2 - 1

2 = a - 1

a = 3

Therefore, the equation of the quadratic in vertex form is y = 3(x - 4)^2 - 1. Therefore, option A is correct.