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

x²-16 should be easily spotted as the difference of two squares
so square root 16 and x
so you get x+4
then you have one other set of brackets to give -16 and 0 x's
difference of two squares it the same numbers different signs so for example

Answer 2

Yes thank you, I actually already had gotten the first though. The one that I was having trouble with was finding x2 = -2x + 24

Answer 3

x²=-2x+24

add 2x to both sides and subtract 24 from both sides to make this equal to 0

x²+2x-24=0

now we shall factorise this
multiply -24 by coefficient of x²
1x-24=-24

we need two numbers to add up to coefficient of x which is 2 and multiply to give -24

+6 and -4 work for this solution

now replace 2x with +6x and -4x to get

x²+6x-4x-24

take out the factor in each

x(x+6)-4(x+6)

(x-4)(x+6)

Answer 4

Part 2: Describe what the solution(s) represent to the graph of each.
(x+4)(x-4)
this graph means that the graph crosses the x axes at two points
x+4=0
x=-4
this cuts at -4 on the x axes
x-4=0
x=4

this cuts at 4 on the x axes
so it cuts x axes at 4 and -4

(x-4)(x+6)
this graph cuts at
x-4=0
x=4
x+6=0
x=-6
this cuts at 4 and -6 on the x axes

Answer 5

Thank you so much that helped a lot!

Answer 6

Part 3
they are both positive x squared so they have the same shape (positive parabola i think it is called)
they both cut at 4 on the x axes
they are different because the second equation cuts at -6 rather than -4