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

Answer:

Listed below

Step-by-step 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:

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

We know that in this case:

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

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

$Xv=\frac{-(-5)}{2.1} =\frac{5}{2}=2.5$

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

$f(x=\frac{-5}{2})=(\frac{-5}{2}) ^{2} -5.\frac{-5}{2}-6=\frac{51}{4}=12.75$

So we know now that

$Xv=\frac{-5}{2}$ and $Yv=\frac{51}{4}$

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:

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

This means that this formula can have two posisible solutions:

$x= \frac{5+7}{2} =\frac{12}{2}=6$

Or:

$x= \frac{5+7}{2} =\frac{-2}{2}=-1$

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