+1124 Hi friends,
My stepdaughter came to me today explaining a sum she got in the exam. I believe I have understood her right, so here is the problem....I did some of it..
\(f(x)=a(x+2)^2+c\)
\(g(x)=(2x+5)(x+b)\)
Nothing else is given. Calculate a, b and c. Apparently both equations point to the one and same parabola.
So I said:
The axis of simmetry lies on \(x=-2\)
The x intercepts are \(x=-{5 \over 2}\) and \(x=-b\)
Now since the one x intercept lies on -2.5, and the axis of simmetry is on the x=-2, it tells me the other x intercept has to be -1.5
So, \(b=1.5 \)
From here I'm stuck. Please help me with this...as usual, all help is greatly appreciated!
Ax^2 +4ax+ 4a+c And
2x^2 +x(5+2b) +5b Are supposed to be the same
a=2 5+2b=4a So b = 3/2 4a+c=5b So c = You can finish from here i am sure
+118608 hi Juriemagic,
If they are the same parabola then they are the same equation.
You need to check the answer, 
\(f(x)= a(x^2+4x+4)+c\\ f(x)= ax^2+4ax+(4a+c)\\~\\ g(x)=2x^2+(2b+5)x+5b\\~\\ \text{equate coefficients}\\ a=2\\~\\ 2b+5=4a\\ 2b+5=8\\ 2b=3\\ b=1.5\\ \\~\\ 4a+c=5b\\ 8+c=7.5\\ c=-0.5\\ \)
