Question 1036392
"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

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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