Question

PLEASE HELP!!!!!!!!

Answer 1

Answer:

9

Step-by-step explanation:

A quadratic equation is

$ax^{2} +b+c$

The axis of symmetry is 1. This means that some value of

-b/2a =1.

f(0) represent one of the horinzontal roots. Since f(0) equal 0, the constant is 0.

Notice how x=1 is the line of symmetry. This means when x=4 and x=-2, the quadratic is equal. so consider this equation.

$a(4)^{2} +b(4)= a(-2)^{2} +b(-2)$=-24

16a+4b= -24

4a-2b=-24

Solve for a by elimination.

2(4a-2b=-24)= 8a-4b=-48

Add both equations.

(16a+4b=-24)+(8a-4b=-48)= 24a=-92

Solve for a.

24a=-92

a=-3

Subsitute to in for b.

16(-3)+4b=-24

-48+4b=-24

4b=24

b=6

This means a=-3

b=6

So b-a is

6+3=9

Answer 2

Answer:  3

Step-by-step explanation:                                                                                                          

$\displaystyle\ \Large \boldsymbol{} We \ have \ a \ square\ function \\\\ f(x)=ax^2+bx+c \\\\And \ we \ know \\\\ \left[\left \[ {{f(0)=a\cdot 0+b\cdot0+c=0} \atop {f(-4)=a(-4)^2+-4b+c=-24}} \right.=>$                                                $\displaystyle\ \Large \boldsymbol{} \left[ \ {{c=0} \atop {16a-4b=-24}} \right. =>\boxed{4a-b=-6} \\\\\\ and \ x_0 =-\frac{b}{2a}=1 =>\boxed{ b=-2a} \\\\\\ \left \{ {{4a-b=-6} \atop {b=-2a}} \right. =>4a+2a=-6=> a=-1 \ ; \ b=2 \\\\\\then \ b-a=2-(-1)=\boxed{3}$