Question

How do you find the vertex of a parabola `y=2x^2 + 8x + 5`?

Answer 1

Vertex (h,k) = (-2,-3)

Explanation:

The vertex of parabola is also known as the maximum or minimum value of the quadratic equation. There are four different ways to find out the vertex of quadratic equation which you can learn from this link .

Here we are going to find the vertex of quadratic equation by converting it too vertex form of an equation.

The vertex form of an equation is given by;

`y = a(x - h)^2 + k`.........equation 1

where (h,k) is the vertex of an equation,

Now, we have;
`y=2x^2+8x+5`

Note: Here we need to convert the x variables into perfect square.

or, `y=2x^2+8x+5`

First take out 2 as common factor from first two variables, we get

or, `y=2(x^2+4x)+5`
or, `y=2(x^2+2XxX2 + 2^2 -2^2)+5`

Please remember the algebraic formula `(a+b)^2 = a^2+2ab+b^2`

or, `y=2((x+2)^2 -4)+5`

Open bracket with 2, we get

or, `y=2(x+2)^2 - 8+5`
or, `y=2(x+2)^2 - 3`
or, `y=2(x-(-2))^2 +(- 3)`..............equation 2

Now we have equation 2 as vertex form of an equation. This method is used to convert quadratic equation into vertex form of an equation.

Now, comparing equation 1 and 2, we get
(h,k) = (-2,-3)

Thanks

Answer 2

`y = 2x^2 + 8x + 5`

Explanation:

x-coordinate of vertex: `x = (-b/(2a)) = -8/4 = -2`
y-coordinate of vertex: `y = f(-2) = 8 - 16 + 13 = -3`
`Vertex: (-2, -3)`