Question

Re-write the quadratic function below in Standard Form

y=-4(x+5)^2+4

Answer 1

Standard form

• ax²+bx+c=0

`\\ \rm\rightarrowtail y=-4(x+5)^2+4`

`\\ \rm\rightarrowtail y=-4(x^2+10x+25)+4`

`\\ \rm\rightarrowtail y=-4x^2-40x-100+4`

`\\ \rm\rightarrowtail y=-4x^2-40x-96`

Answer 2

`y=-4x^2-40x-96`

Explanation:

Standard form of a quadratic function:
`y=ax^2+bx+c`

Given function:

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

Apply Perfect Square formula
`(a+b)^2=a^2+2ab+b^2` to
`(x+5)^2`

`\implies y=-4(x^2+10x+25)+4`

Expand brackets:

`\implies y=-4x^2-40x-100+4`

Simplify:

`\implies y=-4x^2-40x-96`