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Question 450318: find the x-intercepts of the parabola with vertex (-5,80) and y intercept (0,-45)
round to the nearest hundreth
i have no idea how to do this problem please help!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the x-intercepts of the parabola with vertex (-5,80) and y intercept (0,-45)
round to the nearest hundreth
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Standard form for a parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
For given problem, (h,k)=(-5,80).
We can then use point (0,-45) for x and y to solve for A
-45=A(0+5)^2+80
-45=A(25)+80
25A=-45-80=-125
A=-5
Equation of given parabola:
y=-5(x+5)^2+80
solving for x-intercepts (also known as roots or zeros)
Set y=0, then solve for x
0=-5(x+5)^2+80
-5(x+5)^2=-80
(x+5)^2=-80/-5=16
Taking sqrt of both sides
x+5=±√16=±4
x=-5-4=-9
or x=-5+4=-1
ans:
x-intercepts of given parabola: -9 or -1
See graph below to visually relate to the algebra above: (Note the y-intercept, and the two x-intercepts seen in the graph
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