Question

Define a quadratic function y=f(x) that satisfies the given conditions,

Vertex (5, -1) and passes through (0, -76).

f(x)= _____

Answer 1

Answer:

f(x) = -3(x-5)^2 - 1

Step-by-step explanation:

Answer 2

Answer:

The quadratic function f(x)=15x-76

Solution:

As given in the problem, the two points are $(x_1,y_1) = (5,-1)$ and $(x_2,y_2) = (0,-76)$

We know the slope $\mathrm{m}=\frac{y_2-y_1}{x_2-x_1}$

Now substituting the value of points we get,

$\text { Slope } m=\frac{-76-(-1)}{0-5}=\frac{-76+1}{-5}=\frac{75}{5}=15$

We know the equation of a line at a given point $(x_1, y_1)$ is $(y-y_1) = m(x-x_1)$

Let us take the point (5,-1) for the equation, then we get

$\Rightarrow(y-(-1)) = m\times(x-5)$

Multiplying the signs,

$\Rightarrow(y+1) = 15\times(x-5)$

$\Rightarrow y+1 = 15x- 75$

$\Rightarrow y = 15x -75 -1$

$\Rightarrow y = 15x -76$

Hence, the function f(x) is $y = 15x-76$