F(x + 1) = (5/2)*f(x)

f(x + 1) = 2.5*f(x), f(1) = 3.2

f(2) = 2.5f(1) = 2.5*3.2 = 8

<span>f(3) = 2.5f(2) = 2.5*8 = 20
</span>
f(4) = 2.5f(3) = 2.5*20 = 50

<span>f(5) = 2.5f(4) = 2.5*50 = 125</span>

8 0

3 years ago

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The graph of a quadratic function has a vertex at (5,3) and goes through the point (-1,-9). What is the equation of the function

kotegsom [21]

Answer:

$y=-\frac{1}{3} (x-5)^2+3$

Step-by-step explanation:

We are given the following;

Vertex of a quadratic function = (5,3)
A point where the function passes through (-1, -9)

Required to determine the equation of the function;

We need to know the vertex form of a quadratic function is;

$y=a(x-h)^2+k$ , where h and k correspond to the vertex (h,k)

Therefore, we can replace the variables h and k of the vertex in the equation;

That is;

$y=a(x-5)^2+3$

Then we use the equation and the point given to solve for a

x = -1 and y = -9

We get;

$-9=a(-1-5)^2+3\\-9 = a(36) + 3\\-9 - 3 = 36a\\-12 =36a \\a=-\frac{1}{3}$

Substituting the values of a, h and k in the equation, we get;

$y=-\frac{1}{3} (x-5)^2+3$

Thus, the equation of the function in the vertex form is $y=-\frac{1}{3} (x-5)^2+3$

8 0

3 years ago