SOLUTION: Begin with the parent y = x² graph. Show how to transform it to graph the function below. y = -2(x + 1)² + 1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Begin with the parent y = x² graph. Show how to transform it to graph the function below. y = -2(x + 1)² + 1      Log On


   

Question 941392: Begin with the parent y = x² graph. Show how to transform it to graph the
function below.
y = -2(x + 1)² + 1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
start with:
y+=+x%5E2+
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%29+

now, multiply coefficient of x%5E2+ by -2
y+=+-2x%5E2+
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%5E2%29+
f%28x%29 flipped upside down ("reflected about the x-axis") and the parabola for -2x%5E2+ grows twice as fast as x%5E2, so its graph is "squeezed"
now add 1 to x and square it
y+=+-2%28x+%2B+1%29%5E2+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2%28x%2B1%29%5E2%29+

as you can see entire graph is moved one unit to the left

now add 1 to y+=+-2%28x+%2B+1%29%5E2+
y+=+-2%28x+%2B+1%29%5E2+%2B1

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2%28x%2B1%29%5E2%2B1%29+
as you can see entire graph is moved one unit up

so, in short the parent function graph was:
1. flipped upside down ("reflected about the x-axis") and squized
2. moved one unit to the left
3. moved one unit up