SOLUTION: Suppose a parabola has a vertx (-1,8) and y-intercept 7 How do you find the function f whose graph is this parabola and express f in the form f(x)= {{{ax^2+bx+c}}}?

Question 223764: Suppose a parabola has a vertx (-1,8) and y-intercept 7
How do you find the function f whose graph is this parabola and express f in the form f(x)= ?
Found 2 solutions by stanbon, MLipsky:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose a parabola has a vertx (-1,8) and y-intercept 7
How do you find the function f whose graph is this parabola and express f in the form f(x)= ?
-----------------------------------
Vertex form: y-k = a(x-h)^2
---
h=-1,k=8, y=7 when x = 0
--------------
7-8 = a(0+1)^2
-1 = a
------------------
Equation:
y-8 = -1(x+1)^2
y = -(x^2+2x+1)+8
f(x) = -x^2-2x+7
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Cheers,
Stan H.
Answer by MLipsky(9) (Show Source): You can put this solution on YOUR website!
You can write a quadratic equation in "vertex form":
, where the vertex is (h, k).

The answer will still have "x" and "y" in the equation, so we just need to find the "a", "h" and "k".
You already have the "h" and "k" (from the vertex). So, let's plug them in:

(simplified)

Looking good, but we still need "a". Now, where in the world are we going to find THAT???

Wait. I have an idea. They said the y-intercept is 7. In other words, it crosses the y-axis at y=7. Hey! They just gave us another ordered pair: (0, 7).

Let's plug that in:
(plugged in)

Now we have all three pieces of our puzzle:
a=-1
h=-1
k=8

Plug in the pieces:
(Notice that the answer still has "x" and "y" in the equation.)

Oops! They want the answer in standard form. No problem.

(squared the (x+1) )
(F.O.I.L.)
(distributed the -1)
(added 8 to both sides)

Let's graph it just to be sure the vertex is at (-1, 8) and y-intercept is at 7.

Shazam! It checks out.

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