Question

Write a quadratic function in vertex form whose graph has the vertex

Answer 1

Answer:

y = $\frac{1}{2}$(x - 5)² - 2

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (5, - 2), thus

y = a(x - 5)² - 2

To find a substitute (7, 0) into the equation

0 = a(7 - 5)² - 2

0 = 4a - 2 ( add 2 to both sides )

2 = 4a ( divide both sides by 4 )

a = $\frac{2}{4}$ = $\frac{1}{2}$

y = $\frac{1}{2}$ (x - 5)² - 2 ← in vertex form