Question 79052: I need help to write an equation of a quadratic function whose graph is a parabola that has a vertex (-3,7) and that passes through the origin. Please.
Found 2 solutions by funmath, Edwin McCravy:
Answer by funmath(2933)   (Show Source):
Answer by Edwin McCravy(20064)  (Show Source):
You can put this solution on YOUR website!
I need help to write an equation of a quadratic function
whose graph is a parabola that has a vertex (-3,7) and
that passes through the origin. Please.
The standard form of a parabola with vertex (h,k) is
y = a(x - h)² + k
where (h, k) is its vertex.
Since its vertex is (-3,7) we substitute -3 for h and 7 fo k.
y = a(x - (-3) )² + 7
y = a(x + 3)² + 7
Since it passes through the origin, which is the point
(x,y) = (0,0), if we substitute that point into the equation,
the equation must be satisfied, So we substitute that point
by substituting 0 for x and 0 fot y:
y = a(x + 3)² + 7
0 = a(0 + 3)² + 7
0 = a(3)² + 7
0 = a(9) + 7
0 = 9a + 7
add -9a to both sides
-9a = 7
divide both sides by -9
a = -7/9
So now we go back to
y = a(x + 3)² + 7
and replace a by (-7/9)
y = (-7/9)(x + 3)² + 7
Your teacher may accept it that way, or you
can clear of fractions by multiplying
through by the LCD = 9
9y = -7(x + 3)² + 63
9y = -7(x + 3)(x + 3) + 63
9y = -7(x² + 3x + 3x + 9) + 63
9y = -7(x² + 6x + 9) + 63
9y = -7x² - 42x - 63 + 63
9y = -7x² - 42x, which you could write as 7x² + 42x + 9y = 0
or if you didn't want to do that you could
Factor out -7x on the right
9y = -7x(x + 6)
Divide through by 9
y = -7(x + 6)/9
There are lots of ways you could leave the answer.
Edwin
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