Question

Hello, I’m stuck on this problem and need some help please

Answer 1

Given

The function is given as

`f(x)=5x^2+2x-3`Step-by-step explanation

a. To determine the x-intercepts of the function

Substitute the y -coordinate equal to 0.

`5x^2+2x-3=0`

Factorize the equation.

`\begin{gathered} (x-(3)/(5))(x+1)=0 \\ x=(3)/(5),-1. \end{gathered}`Answer

The x-intercepts are

`x=(3)/(5),-1`

b. The vertex of the function is determined as

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

Substitute the values.

`x=-(2)/(5*2)=-0.2`

Now substitute the value of x in the function.

`\begin{gathered} 5(-0.2)^2+2(-0.2)-3=f(-0.2) \\ 5*0.04-0.4-3=f(-0.2) \\ 0.2-0.4-3=-3.2 \end{gathered}`Answer

The coordinates of vertex is

`(-0.2,-3.2)`

The condition for vertex to be maximum or minimum,

If a>0, the parabola opens upward and the vertex is a minimum.

If a<0, the parabola opens downward, and the vertex is a maximum.

As a for he given function is 5 which is positive.

Then the vertex is a minimum.

c. The steps for graph the function.

We know the x-intercepts of the function and substitute in the graph.

Also plot the points of the vertex in the graph.

Answer

Then the graph is determined as