Question

Find the zeros of each functions by using a graph and a table. F(x)=2x^2+2x-24.

Answer 1

Given the function

`f(x)=2x^2+2x-24`

To find the x and y intersects of the parabola you have to do as follows:

y-intercept

This is the value of f(x) when x=0, to find it replace the value in the formula:

`\begin{gathered} f(0)=2(0)^2+2\cdot0-24 \\ f(0)=-24 \end{gathered}`

The y-intercept of the parabola is (0,-24)

Vertex

Calculate the x coordinate using the following formula:

For

`y=ax^2+bx+c`
`x_v=-(b)/(2a)`

For this function:

`x_v=-(2)/(2\cdot2)=-(2)/(4)=-(1)/(2)`

Using this value of x imput it in the formula to reach the value of the y-coordinate of the vertex:

`\begin{gathered} f(x_v=-(1)/(2))=2(-(1)/(2))^2+2(-(1)/(2))-24 \\ f(x_v)=-(49)/(2) \end{gathered}`

The vertex is (-1/2,-49/2)

Using these two points you can draw the function:

Using the graph you can determine the x-intercepts of the function, these are (-4,0) and (3,0)