Question 732022: Writing an equation for a parabola in the form y= a(x-h)^2 + k with given information.
1. It gives you :
with y- intersept 10, x- intercept 2, and equation of axis of symmetry x-3=0
how would i find a and k?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Writing an equation for a parabola in the form y= a(x-h)^2 + k with given information.
1. It gives you : with y- intersept 10, x- intercept 2, and equation of axis of symmetry x-3=0
how would i find a and k?
***
Standard form of equation for a parabola: y=a(x-h)^2+k, (h,k)=(x,y) coordinates of vertex, a=multiplier which affects slope or steepness of curve
Equation of axis of symmetry: x-3=0
x=3
so, h=3
Equation: y=a(x-3)^2+k
points given:
y-intercept: (0,10)
x-intercept: (2,0)
using points to form a system of two equations to solve for a and k
..
10=a(0-3)^2+k
0=a(2-3)^2+k
..
10=9a+k
0= a +k
subtract
10=8a
a=10/8=5/4
k=-a=-5/4
Equation:
y=(5/4)(x-3)^2-5/4
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