Answer:
Let's see what to do buddy..
Step-by-step explanation:
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STEP (1)
We know that the quadratic functions form are like this :
[tex]y = a \: {x}^{2} + b \: x + c [/tex]
The quadratic function opens upward so ;
[tex]a > 0[/tex]
The axis of parabolic symmetry passes through the vertex of the parabolic.
So we know that x vertex is equal to -2.
The vertex's x is finding from this equation:
[tex]x = - \frac{b}{2a} \\ [/tex]
So we have :
[tex] - 2 = - \frac{b}{2a} \\ [/tex]
Multiply the sides of the equation by 2a :
[tex]b = 4a[/tex]
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STEP (2)
A quota passes through points (-3,2) and (0,11) , so points (-3,2) and (0,11) must be true in the quota equation.
[tex]y = f(x) = a{x}^{2} + bx + c \\ \\b = 4a \\ \\ y = f(x) = a {x}^{2} + 4ax + c [/tex]
[tex]f( - 3) = 2 \\ \\ a ({ - 3})^{2} + 4a( - 3) + c = 2 \\ \\ 9a - 12a + c = 2 \\ \\ - 3a + c = 2 \\ \\ \\ \\ f(0) = 11 \\ \\ a ({0})^{2} + 4a(0) + c = 11 \\ \\ c = 11 [/tex]
[tex] - 3a + c = 2 \\ \\ c = 11 \\ \\ - 3a + 11 = 2 \\ 11 \: goes \: to \: the \: other \: side \: \\ \\ - 3a = 2 - 11 \\ - 3a = - 9 \\ divided \: the \: sides \: of \: the \: equation \: by \: - 3 \\ a = 3[/tex]
And we're done.
Thanks for watching buddy good luck.
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