SOLUTION: A quadratic function f(x) with different values of x, -4,-8 -2,-6 0,0 2,10 f(x) has a line of symmetry at x=-4 What other value of x is f(x) equals to 0?

Algebra ->  Graphs -> SOLUTION: A quadratic function f(x) with different values of x, -4,-8 -2,-6 0,0 2,10 f(x) has a line of symmetry at x=-4 What other value of x is f(x) equals to 0?       Log On


   

Question 761846: A quadratic function f(x) with different values of x,
-4,-8
-2,-6
0,0
2,10
f(x) has a line of symmetry at x=-4
What other value of x is f(x) equals to 0?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
We know that a quadratic equation will be in the form:
y+=+ax%5E2+%2B+bx+%2B+c
Our job is to find the values of a, b and c, and we can do it using three given points:
-2,-6=x,y
-6+=+a%28-2%29%5E2+%2B+b%28-2%29+%2B+c
-6+=+4a+-+2b+%2B+c.......eq.1
0%2C0
0+=+a%280%29%5E2+%2B+b%280%29+%2B+c
highlight%280+=+c%29.....eq.2

2%2C10
10+=+a%282%29%5E2+%2B+b%282%29+%2B+0
10+=+4a+%2B+2b+.....eq.3
go back to -6+=+4a+-+2b+%2B+c.......eq.1 plug in c=0
-6+=+4a+-+2b+%2B0.......eq.1
-6+=+4a+-+2b+.......eq.1

now solve the system
-6+=+4a+-+2b+.......eq.1
10+=+4a+%2B+2b+.....eq.3
___________________________...subtract eq.1 from eq.3
10-%28-6%29+=+4a+%2B+2b-4a-%28-2b%29+
10%2B6+=+2b%2B2b+
16+=+4b+
16%2F4+=+b+
highlight%284+=+b%29+
now find a
-6+=+4a+-+2%2A4+.......eq.1
-6+=+4a+-+8+
-6+%2B8=+4a+
2=+4a+
2%2F4=a+
highlight%281%2F2=a%29+
so, our equation is:
y+=+%281%2F2%29x%5E2+%2B4x+%2B+0
y+=+%281%2F2%29x%5E2+%2B4x



as you can see on a graph, other value of x where f%28x%29=0 is x=-8
we can check it solving y+=+%281%2F2%29x%5E2+%2B4x
0=+%281%2F2%29x%5E2+%2B4x.....both sides multiply by 2
0%2A2=+2%281%2F2%29x%5E2+%2B2%2A4x
0=+x%5E2+%2B8x....factor

0=+x%28x+%2B8%29
solutions:
0=+x
or if %28x+%2B8%29=0 => x=-8