Question

Write the vertex form of the equation of the parabola that has a vertex of (-6,-5) and passes through the point (-8,6)

Answer 1

y =
`(11)/(4)`(x + 6)² - 5

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) = (- 6, - 5), thus

y = a(x + 6)² - 5

To find a substitute (- 8, 6) into the equation

6 = a(- 2)² - 5

6 = 4a - 5 ( add 5 to both sides )

11 = 4a ( divide both sides by 4 )

a =
`(11)/(4)`, thus

y =
`(11)/(4)`(x + 6)² - 5 ← in vertex form