Question

Part 1: Solve each of the quadratic equations below. Show your work.

x2 − 16 = 0 and x2 = −2x + 24

Part 2: Describe what the solution(s) represent to the graph of each.

Part 3: How are the graphs alike? How are they different?

Answer 1

(x-4)(x+4) = 0
x = 4 or x = -4
x2 + 2x -24 = 0
(x+6)(x-4) = 0
x = -6 or x = 4
The graphing of the solutions shows that they have 1 solution in common: x=4

Answer 2

\[x^{2}-16=0,x ^{2}=16,x=\pm4.\]
\[x^{2}=-2x+24,x ^{2}+2x-24=0,x ^{2}+6x-4x-24=0,\]
or x(x+6)-4(x+6)=0
or (x+6)(x-4)=0
Either x+6=0,gives x=-6
Or x-4=0, gives x=4
Solution is x=-6, x=4

Answer 3

l..L.et f(x)=x^2-16
Again Let f(x)=x^2+2x-24=x^2+2x+1-25
f(x)=(x+1)^2-25
f(x)+25=X^2,which is a parabola with vertex at(-1,-25)
Two graphs are parabolas
They are alike.