SOLUTION: A quadratic function has a minimum of -8 and an x-intercept of -5. Its axis of symmetry is x=-3. Find the y-intercept of this quadratic function.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A quadratic function has a minimum of -8 and an x-intercept of -5. Its axis of symmetry is x=-3. Find the y-intercept of this quadratic function.      Log On


   

Question 1128838: A quadratic function has a minimum of -8 and an x-intercept of -5. Its axis of symmetry is x=-3. Find the y-intercept of this quadratic function.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
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A quadratic function has a minimum of -8 and an x-intercept of -5. Its axis of symmetry is x=-3. Find the y-intercept of this quadratic function.
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The other x-intercept is -1.

y=a%28x%2B5%29%28x%2B1%29

point (-3, -8) was described.

a%28-3%2B5%29%28-3%2B1%29=-8
a%282%29%28-2%29=-8
a%28-4%29=-8
a=2


highlight%28y=2%28x%2B5%29%28x%2B1%29%29

Find y-intercept:
y=2%285%29%281%29

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

A quadratic function has a minimum of -8 and an x-intercept of -5. Its axis of symmetry is x=-3. Find the y-intercept of this quadratic function.
Vertex form of a parabola: matrix%281%2C3%2C+y%2C+%22=%22%2C+a%28x+-+h%29%5E2+%2B+k%29

matrix%281%2C3%2C+0%2C+%22=%22%2C+a%28-+5+-+-+3%29%5E2+-+8%29 ------- Substituting (- 3, - 8) for (h, k), and (- 5, 0) for (x, y)

0 = 4a - 8

8 = 4a

matrix%281%2C5%2C+a%2C+%22=%22%2C+8%2F4%2C+%22=%22%2C+2%29

We now get: matrix%281%2C3%2C+y%2C+%22=%22%2C+2%28x+%2B+3%29%5E2+-+8%29

matrix%281%2C3%2C+y%2C+%22=%22%2C+2%280+%2B+3%29%5E2+-+8%29 ------- Substituting 0 for x