Question

HELP WILL MARK BRAINLIEST!!!

Answer 1

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 :

$y = a \: {x}^{2} + b \: x + c$

The quadratic function opens upward so ;

$a > 0$

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:

$x = - \frac{b}{2a}$

So we have :

$- 2 = - \frac{b}{2a}$

Multiply the sides of the equation by 2a :

$b = 4a$

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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.

$y = f(x) = a{x}^{2} + bx + c \\ \\b = 4a \\ \\ y = f(x) = a {x}^{2} + 4ax + c$

$f( - 3) = 2 \\ \\ a ({ - 3})^{2} + 4a( - 3) + c = 2 \\ \\ 9a - 12a + c = 2 \\ \\ - 3a + c = 2 \\ \\ \\ \\ f(0) = 11 \\ \\ a ({0})^{2} + 4a(0) + c = 11 \\ \\ c = 11$

$- 3a + c = 2 \\ \\ c = 11 \\ \\ - 3a + 11 = 2 \\ 11 \: goes \: to \: the \: other \: side \: \\ \\ - 3a = 2 - 11 \\ - 3a = - 9 \\ divided \: the \: sides \: of \: the \: equation \: by \: - 3 \\ a = 3$

And we're done.

Thanks for watching buddy good luck.

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