SOLUTION: A quadratic function has a vertex at (-3,4) and a y-intercept at 1. What is the vertical stretch factor ? I'm guessing 1/3 or 3 but I'm not sure :( Please help me :)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A quadratic function has a vertex at (-3,4) and a y-intercept at 1. What is the vertical stretch factor ? I'm guessing 1/3 or 3 but I'm not sure :( Please help me :)      Log On


   

Question 118943: A quadratic function has a vertex at (-3,4) and a y-intercept at 1. What is the vertical stretch factor ? I'm guessing 1/3 or 3 but I'm not sure :( Please help me :)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
vertex at (-3,4)..=> h=-3 and k=4
y-intercept at y=1
we will need to use this formula to find a:
h=+-b%2F2a}


First use vertex form to find b:
y+=+a%28x-h%29%5E2+%2B+k
1=+a%28x-%28-3%29%29%5E2+%2B+4
1-+4+=+a%28x+%2B3%29%5E2+
-+3+=+a+%28x%5E2+%2B6x++%2B9%29+
a+=+%28x%5E2+%2B6x++%2B9%29%2F%28-3%29+

a+=+%281%2F3%29x%5E2+%96+2x++-3……………………b=-2

Now use the formula h=+-b%2F2a to find a:
h=+-b%2F2a
2a=+-b%2Fh
a=+-b%2F%282h%29

a=+-b%2F%282%28-3%29%29
a=+-%28-2%29%2F%282%28-3%29%29
a=+2%2F-6
a=+-%281%2F3%29…………… the stretch/compression factor
Here is the graph:
Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

Error: the leading coefficient "a" cannot be equal to zero.