Question

Y=2x^2+2x-4 find the vertex and explain why

Answer 1

`( - 0.5 , - 4.5 )`

Explanation:

Rewrite the equation in vertex form.

Complete the square for

`2 {x}^(2) + 2x - 4`

Use the form

`a {x}^(2) + bx + c`

to find the values of a, b, and c.

a = 2

b = 2

c = −4

Consider the vertex form of a parabola.

`a(x + d) ^(2) + e`

Find the value of d using the formula

`d = (b)/(2a)`

`d = (1)/(2)`

Find the value of e using the formula

`e = c - \frac{ {b}^(2) }{4a}`

`e = - (9)/(2)`

Substitute the values of a, d, and e into the vertex form

`2(x + (1)/(2) ) ^(2) - (9)/(2)`

Set y equal to the new right side.

`y = {2(x + (1)/(2)) }^(2) - (9)/(2)`

Use the vertex form,

`y = a(x - h) ^(2) + k`

to determine the values of a, h, and k.

a = 2

h = -1/2

k = -9/2

Find the vertex (h,k).

`( - (1)/(2) , - (9)/(2) )`