SOLUTION: determine the quadratic equation for the parabola.maxium value:6 ; x-intercept : -2 and 4

Question 88052: determine the quadratic equation for the parabola.maxium value:6 ; x-intercept : -2 and 4
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
determine the quadratic equation for the parabola.maximum value:6 ; x-intercept : -2 and 4
:
Here is one way to do it:
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Max value occurs at the vertex, which is the axis of symmetry, which is half way
between the x intercepts: 4 -(-2) = 6 divide by 2 = 3, and add to -2; x = +1
Vertex: x=+1, y=+6
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In the form ax^2 + bx + c = y, substitute for x and y.
:
Three coordinates gives us 3 equations
:
1. TheVertex: x=1, y=6: 1a + 1b + c = 6
2. intercept: x=-2,y=0: 4a - 2b + c = 0
3. intercept: x=4, y=0: 16a + 4b + c = 0
:
Three equations, three unknowns, a, b, c.
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Mult eq1 by 2 and add to eq2:
2a + 2b + 2c = 12
4a - 2b + c = 0
-----------------adding eliminates b
6a + 3c = 12
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Mult eq2 by 2 and add to equation 3:
8a - 4b + 2c = 0
16a + 4b + c = 0
----------------adding eliminates b again
24a + 3c = 0
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Take these two resulting 2 unknown equations and:
24a + 3c = 0
6a + 3c = 12
--------------subtracting eliminates c, gives a
18a = -12
a = -12/18
a = -2/3
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Use the equation 6a + 3c = 12, substitute for a and find c:
6(-2/3) + 3c = 12
-4 + 3c = 12
3c = 12 + 4
c = 16/3
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Find b, use eq1, substitute for a & c
a + b + c = 6
(-2/3) + b + (16/3) = 6
+14/3 + b = 6; (6 = 18/3)
b = (18/3) -(14/3)
b = +4/3
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The equation: y = (-2/3)x^2 + (4/3)x + (16/3)
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Checked it using a graphing calc; Graph looked like this:

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Seeing it on a graph should make it more understandable to you, did it?
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