Question

Find the coordinate of the vertex of the following parabola algebraically. y=2x^2-28x+80

Answer 1

vertex = (7, - 18)

Explanation:

given a parabola in standard form : ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

y = 2x² - 28x + 80 is in standard form

with a = 2, b = -28 and c = 80, hence

`x_(vertex)` = -
`(-28)/(4)` = 7

substitute x = 7 into the equation for corresponding value of y

y = 2(7)² - 28(7) + 80 = 98 - 196 + 80 = - 18

vertex = (7, - 18)