SOLUTION: Find the x-intercepts for the graph of the equation y = x^2 + 4x - 45

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Question 168264: Find the x-intercepts for the graph of the equation
y = x^2 + 4x - 45
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Given eqn,
y+=+x%5E2+%2B+4x+-+45
Remember quadratic function --->ax%5E2%2Bbx%2Bc=0
To have a clearer picture of the graph,
We first find the x-coordinate of the vertex with the formula: x=-b%2F2a
x=-4%2F%282%29%281%29 ----> x=cross%28-4%292%2Fcross%282%291
x=-2, x-coordinate of vertex
.
Then for the y-coordinate:
f%28-2%29=y=-2%5E2%2B4%28-2%29-45=4-8-45
y=-49, y-coordinate of vertex
VERTEX -----> (-2,-49)
.
Now for the y-intercept: let x=0 ---> f%280%29=0%2B4%2A0-45=-45
Solving or the x-intercept, via our eqn:
x%5E2%2B4x-45=0, factor out, perfect square
%28x%2B9%29%28x-5%29=0
x-intercepts----system%28highlight%28x=-9%29%2Chighlight%28x=5%29%29
See graph below,
----> ALL INTERCEPTS are marked: GREEN circle=y-intercept and BLUE circle=x-intercepts with BLACK circle as VERTEX (-2,-49)
.
Thank you,
Jojo