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

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

Explanation:

Answer 2

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}=(y_2-y_1)/(x_2-x_1)`

Now substituting the value of points we get,

`\text { Slope } m=(-76-(-1))/(0-5)=(-76+1)/(-5)=(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*(x-5)`

Multiplying the signs,

`\Rightarrow(y+1) = 15*(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`