SOLUTION: From nycmathguy Find any intercepts and test for symmetry. Then sketch the graph of the equation. 1. y = 1 − ∣x∣ 2. x = y^2 − 5

Algebra ->  Decimal-numbers -> SOLUTION: From nycmathguy Find any intercepts and test for symmetry. Then sketch the graph of the equation. 1. y = 1 − ∣x∣ 2. x = y^2 − 5       Log On


   



Question 1182489: From nycmathguy

Find any intercepts and test
for symmetry. Then sketch the graph of the equation.

1. y = 1 − ∣x∣
2. x = y^2 − 5

Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Helping with #1 only.

y=1-abs%28x%29

Two cases occur.
Either x is negative, or x is nonnegative.

Either: y=1-x-----------------when x%3E=0
Or: y=1-%28-x%29-------y=1%2Bx-----when x%3C0

You can continue from that.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find any intercepts and test
for symmetry. Then sketch the graph of the equation.
1. y+=+1+-abs%28x%29
x-intercepts:
0+=+1+-abs%28x%29
abs%28x%29+=+1+=>x=1 or x=-1
y-intercepts:
y+=+1+-abs%280%29
y+=+1+
Replace x with (-x). Simplfy the equation. If the resulting equation is equivalent to the original equation then the graph is symmetrical about the y-axis.
y+=+1+-abs%28-x%29 since abs%28x%29+=+abs%28-x%29, the graph is symmetrical about the y-axis

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+1+-abs%28x%29%29+


2. x+=+y%5E2+-+5
x-intercepts:
x+=+0%5E2+-+5
x+=++-+5
y-intercepts:
0+=+y%5E2+-+5
5=+y%5E2+
y=sqrt%285%29 or y=-sqrt%285%29->exact answer
approximate answer:
y=2.24 or y=2.24


Replace y with -y in the equation
x+=+%28-y%29%5E2+-+5=>x+=+y%5E2+-+5
Since replacing y with -y gives the same equation, x+=+y%5E2+-+5 is symmetric with respect to the x-axis.

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28x%2B5%29%2C-sqrt%28x%2B5%29%29+