SOLUTION: Determine the equation of a parabola with vertex (-2,-11) and point (-4,5)show answer in vertex form.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine the equation of a parabola with vertex (-2,-11) and point (-4,5)show answer in vertex form.      Log On


   

Question 974870: Determine the equation of a parabola with vertex (-2,-11) and point (-4,5)show answer in vertex form.
Found 3 solutions by josgarithmetic, lwsshak3, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
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Standard Form Format, y=a%28x-h%29%5E2%2Bk.

Knowing the vertex and a point for yours, solving for a will allow you to find its value. You already know that (h,k)=(-2,-11).

y-k=a%28x-h%29%5E2
a=%28y-k%29%2F%28x-h%29%5E2
a=%285-%28-11%29%29%2F%28-4-%28-2%29%29%5E2
a=16%2F%28-2%29%5E2
a=4

highlight%28y=4%28x%2B2%29%5E2%2B11%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the equation of a parabola with vertex (-2,-11) and point (-4,5)show answer in vertex form.
vertex form of equation : y=mx+b, m=slope, b=y-intercept
slope ∆y/∆x=(5-(-11))/(-4-(-2))=16/-2=-8
equation: y=-8x+b
solve for b using coordinates of given point (-4,5) on the curve
b=y+8x=5+8*-4=-27
equation=y=-8x-27

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Determine the equation of a parabola with vertex (-2,-11) and point (-4,5)show answer in vertex form.
Vertex form of a parabola: y+=+a%28x+-+h%29%5E2+%2B+k, which becomes: 

5+=+a%28-+4+-+-+2%29%5E2+%2B+-+11

5+=+a%28-+4+%2B+2%29%5E2+-+11

5+=+a%28-+2%29%5E2+-+11

5 = 4a – 11

4a = 5 + 11

4a = 16

a = 16%2F4, or 4

Equation in vertex form: highlight_green%28y+=+4%28x++%2B+2%29%5E2+-+11%29