SOLUTION: Please help with this question. A quadratic function has these characteristics: x = 1 is the equation for the axis of symmetry. x = - 1 is an x-intercept. y = - 4 is the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Please help with this question. A quadratic function has these characteristics: x = 1 is the equation for the axis of symmetry. x = - 1 is an x-intercept. y = - 4 is the      Log On


   

Question 1137546: Please help with this question.
A quadratic function has these characteristics:
x = 1 is the equation for the axis of symmetry.
x = - 1 is an x-intercept.
y = - 4 is the minimum value.
Determine the y-intercept of this parabola.
Explain your thought process.

Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The axis of symmetry is x=1, and one root is x = -1; therefore the other root is 3. So the equation still in factored form is

y+=+a%28x%2B1%29%28x-3%29

To find the value of a, use the fact that the minimum value is at (1,-4):

-4+=+a%281%2B1%29%281-3%29+=+-4a
a+=+1

So the equation is

y+=+%28x%2B1%29%28x-3%29
y+=+x%5E2-2x-3

Then to answer the question that is asked, set x=0 to find that the y-intercept is (0,-3).

graph%28400%2C400%2C-4%2C4%2C-10%2C10%2C%28x%2B1%29%28x-3%29%29

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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A quadratic function has these characteristics:
x = 1 is the equation for the axis of symmetry.
x = - 1 is an x-intercept.
y = - 4 is the minimum value.
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Vertex has x coordinate 1, same as axis of symmetry.
y minimum at -4 means vertex is (1, -4). This given as MINIMUM value of parabola, so equation can be of the form:

y=a%28x-1%29%5E2-4.

x intercept -1 and vertex (1, -4) mean that the other x intercept is 1+2=3; or
y=a%28x%2B1%29%28x-3%29.

Those two formulas for y must be equal.
a%28x-1%29%5E2-4=a%28x%2B1%29%28x-3%29
Solve this for a.
.
.
Let x be 0 in either equation and find y, for y-intercept.