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

Answer:

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

Step-by-step 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:

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