Question

What is the vertex form of `y= 2x^2+7x-15`?

Answer 1

`y=2(x+7/4)^2+169/8`

Explanation:

Given -

`y=2x^2+7x-15`

Find the vertex

`x=(-b)/(2a)= (-7)/(2 xx 2)=-7/4`

`y=2(-7/4)^2+7(-7/4)-15`
`y=2(49/16)-49/4-15`
`y=49/8-49/4-15=169/8`

Quadratic equation in vertex form

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

Where -

`a` is the co-efficient of `x^2`
`h` is `x`coordinate of the vertex
`k` is the `y` coordinate of the vertex

`y=2(x-(-7/4))^2+169/8`
`y=2(x+7/4)^2+169/8`

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