Question

I need help bruv. like asap.

For the function y=x^2 - 5x - 6

(a) Find the vertex

(b) Find the y-intercept

(c) Find the x-intercepts

(Leave your answers in simplified radical form or, where appropriate, round to the nearest hundredth.)

Answer 1

Listed below

Explanation:

This is a cuadratic function excercise.

We know that cuadratic functions have the following formula:

`y=ax^(2) +bx+c`

The graphic of this function will give us a parabola, that can be graphed knowing four points: the two or less x-intercepts, the y-intercept, and the vertex (Xv;Yv).

A) The vertex

The vertex is a point on the graph, so we have to know it's value on the X axis and on the Y axis.

To know the value of Xv we can calculate it using the following formula:

`Xv=(-b)/(2a)`

We know that in this case:

`a=1\\b=-5\\c=-6`

So we supplant said values on the formula and we get:

`Xv=(-(-5))/(2.1) =(5)/(2)=2.5`

To know the value of Yv, we suppland the value of Xv on the function's formula.

`f(x=(-5)/(2))=((-5)/(2)) ^(2) -5.(-5)/(2)-6=(51)/(4)=12.75`

So we know now that

`Xv=(-5)/(2)` and
`Yv=(51)/(4)`

b) The y-intercept is the value of C on the function's formula. We know that c=-6, so

`Y=-6`

c) The x-intercepts can be resolved using the following formula:

`x=\frac{-b+-\sqrt[2]{b^(2)-4ac}  }{2a} \\\\x=\frac{-5+-\sqrt[2]{(-5)^(2)-4.1.(-6)}  }{2.1} \\x=\frac{-(-5)+-\sqrt[2]{25+24}  }{2}\\x=\frac{5+-\sqrt[2]{49}  }{2.1}\\x=(5+-7  )/(2.1)`

This means that this formula can have two posisible solutions:

`x= (5+7)/(2) =(12)/(2)=6`

Or:

`x= (5+7)/(2) =(-2)/(2)=-1`

So that are the X-intercepts: x=6 and x=-1