SOLUTION: In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x^2 to the number of x-intercepts in the graph of g(x) = x^2 -7. Be sure to include the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x^2 to the number of x-intercepts in the graph of g(x) = x^2 -7. Be sure to include the      Log On


   

Question 1140972: In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x^2 to the number of x-intercepts in the graph of g(x) = x^2 -7. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by MathLover1(20849) About Me  (Show Source):
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the number of x-intercepts in the graph of
f%28x%29+=+x%5E2.....set f%28x%29+=0
0=+x%5E2
x=sqrt%280%29
x=0
x-intercepts is at (0,0)

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Cx%5E2%29+

the number of x-intercepts in the graph of
g%28x%29+=+x%5E2+-7.....set g%28x%29+=0
0+=+x%5E2+-7
x%5E2=7
x= ±sqrt%287%29+

x-intercepts is at (sqrt%287%29 ,0) and (-sqrt%287%29 ,0

As you can see, the parent function f(x) is shifted 7 units down and becomes its image g(x).
Therefore, f%28x%29+=+x%5E2 has one x-intercept at (0,0) and+g%28x%29+=+x%5E2+-7+has two x-intercepts at (sqrt%287%29 ,0) and (-sqrt%287%29 ,0)

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Cx%5E2+-7%29+