Question

Y=x2^+9x+7 in vertex form

Answer 1

Answer: (-9/2,-53/4)

Explanation:

Answer 2

`y=\left(x+(9)/(2)\right)^2-(53)/(4)`

Explanation:

Vertex form of a quadratic equation:

`\boxed{y=a(x-h)^2+k}`

where:

• (h, k) is the vertex.
• a is the leading coefficient.

To find the vertex form of a quadratic equation, complete the square.

Given quadratic equation:

`y=x^2+9x+7`

Add and subtract the square of half the coefficient of the term in x to the right side of the equation:

`\implies y=x^2+9x+\left((9)/(2)\right)^2+7-\left((9)/(2)\right)^2`

`\implies y=x^2+9x+(81)/(4)+7-(81)/(4)`

`\implies y=x^2+9x+(81)/(4)-(53)/(4)`

Factor the perfect square trinomial formed by the first 3 terms:

`\implies y=\left(x+(9)/(2)\right)^2-(53)/(4)`