Question

Which is the solution set of the equuation a^2-25=0
A:0,-5
B:0,5
C:-5,5
D:-5,-5

Answer 1

That is a parabola f(x) = a^2 - 25

Setting that to zero f(x) = 0, will give you when y=0, or the x-axis intercepts

Answer 2

since the squared term is +, the thing will open upwards... When a=0, f(a) = -25, that is the y-intercept and the vertex..

Answer 3

The solution set includes those two points when y=0, where it crosses the 'a' axis

Answer 4

I dont get it.

Answer 5

you can solve that with algebra, move the 25 over, square root both sides...

Answer 6

recall,
\[\sqrt{x^2}= \left| x \right| \]

Answer 7

ill show you for this one..
\[a^2 - 25 = 0\]

a^2 = 25

\[\sqrt{a^2}=\sqrt{25}\]
\[ \left| a \right| = 5\]

Answer 8

so a can be +5 or -5

Answer 9

That the answer?

Answer 10

yes, when it asks for the 'solution set'...

You just have to find the values for a here. Solving a^2-25=0 for a

Answer 11

I see

Answer 12

and graphing the thing is a good check...
https://www.desmos.com/calculator

crosses a axis (y=0) when a is +5 and -5


(use x instead of a to graph it

Answer 13

y=x^2-25

Answer 14

Isee. thanks