SOLUTION: The graph of a quadratic function has x intercepts -2 and -7 and passes through the point (1,24). The quadratic equation that has these roots when written in standard form looks li

Algebra ->  Equations -> SOLUTION: The graph of a quadratic function has x intercepts -2 and -7 and passes through the point (1,24). The quadratic equation that has these roots when written in standard form looks li      Log On


   

Question 1036392: The graph of a quadratic function has x intercepts -2 and -7 and passes through the point (1,24). The quadratic equation that has these roots when written in standard form looks like ax square +bx+c=0. What are the values of a,b,c?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The graph of a quadratic function has x intercepts -2 and -7"
means the two solutions are
x = -2 or x = -7
Get everything to one side to get
x+2 = 0 or x+7 = 0
Now use the zero product property to get
(x+2)(x+7) = 0
---------------------------------

So the equation is y = k*(x+2)(x+7) where k helps determine the vertical stretching. This will allow us to force the graph to also go through (1,24)

Plug in x = 1 and y = 24. Then solve for k.

y = k*(x+2)(x+7)
24 = k*(1+2)(1+7)
24 = k*3*8
24 = k*24
24 = 24*k
24*k = 24
24*k/24 = 24/24
k = 1

So k = 1 making y = k*(x+2)(x+7) turn into y = 1*(x+2)(x+7) = (x+2)(x+7)

Now let's expand out (x+2)(x+7)

(x+2)(x+7) = x(x+7)+2(x+7)
(x+2)(x+7) = x^2+7x+2x+14
(x+2)(x+7) = x^2+9x+14

x^2+9x+14 is the same as 1*x^2+9x+14
1*x^2+9x+14 is in the form ax^2+bx+c

where
a = 1
b = 9
c = 14