Find the x and y intercepts for the following parabolas.
y=(x+12)^2-144
y=(x-8)^2-4
x-intercept is obtained by solving for x after setting y=0.
For example:
f(x)=x^2+2x+1
set y=f(x)=0, then
x^2+2x+1=0
(x+1)²=0
x=-1 (x-intercept)
y-intercept is obtained by solving for y after setting x= 0.
For example : f(x)=x^2+2x+1
Set x=0, then
f(x)=y=0^2+2(0)+1=1
y=1 is the y-intercept.
To find the x-intercepts of a parabola, we need to set y equal to zero and solve for x. Similarly, to find the y-intercept, we set x equal to zero and solve for y.
Parabola 1: y = (x + 12)^2 - 144
To find the x-intercepts (or zeros), we set y = 0:
0 = (x + 12)^2 - 144
Now, let's solve for x:
(x + 12)^2 - 144 = 0
Taking the square root of both sides:
√((x + 12)^2 - 144) = √0
(x + 12) - 12 = 0
x + 12 = 0
x = -12
Therefore, the x-intercept for the given parabola is x = -12.
To find the y-intercept, we set x = 0:
y = (0 + 12)^2 - 144
y = 12^2 - 144
y = 144 - 144
y = 0
Therefore, the y-intercept for the given parabola is y = 0.
Parabola 2: y = (x - 8)^2 - 4
To find the x-intercepts (or zeros), we set y = 0:
0 = (x - 8)^2 - 4
Now, let's solve for x:
(x - 8)^2 - 4 = 0
Taking the square root of both sides:
√((x - 8)^2 - 4) = √0
(x - 8) ± 2 = 0
x - 8 = 2 or x - 8 = -2
x = 10 or x = 6
Therefore, the x-intercepts for the given parabola are x = 10 and x = 6.
To find the y-intercept, we set x = 0:
y = (0 - 8)^2 - 4
y = (-8)^2 - 4
y = 64 - 4
y = 60
Therefore, the y-intercept for the given parabola is y = 60.