Graph the function f(x)=x^2+2x-8 what are x intercepts
what are y intercepts
what is maximum or minimum value

Step-by-step explanation:

We need to find the vertex, x-intercepts, and y-intercept to give us an idea of what the graph will look like.

Explanation:

Let's find the vertex first. We can find the x-coordinate by using

x

=

−

b

2

a

:

x

=

−

2

2

⋅

1

=

−

2

2

=

1

The y-coordinate can be found by plugging the x-value back into the equation:

(

1

)

2

−

2

(

1

)

−

8

=

1

−

2

−

8

=

9

The vertex is

(

1

,

9

)

. Next, let's find the x-intercepts, which are the zeroes of the equation. Let's factor the polynomial and find them:

x

2

−

2

x

−

8

=

0

(

x

−

4

)

(

x

+

2

)

=

0

x

−

4

=

0

x

=

4

x

+

2

=

0

x

=

−

2

The x-intercepts are

(

4

,

0

)

and

(

−

2

,

0

)

. Finally, the y-intercept can be found by letting

x

=

0

:

0

2

−

2

(

0

)

−

8

=

−

8

The y-intercept is

(

0

,

−

8

)

. You can plot the bolded points, which will be able to create a decent outline of the parabola, If you need them, you can plot other points on the graph, such as

(

2

,

−

8

)

,  

(

−

1

,

−

5

)

, and

(

3

,

−

5

)

. This is what the graph will look like:

graph{x^2-2x-8 [-9, 11, -10, 1]}

The x intercepts are 2, -4

The y intercept is -8

The minimum is -9

Step-by-step explanation:

f(x)=x^2+2x-8

To find the x intercepts, set equal to zero and factor

0 =x^2+2x-8

0 = (x+4)(x-2)

Using the zero product property

0 = x+4    0 = x-2

x = -4        x = 2

The x intercepts are 2, -4

To find the y intercepts, set x =0 and solve for y

y = 0^2 +2(0) -8

y = -8

The y intercept is -8

Since the coefficient of the x^2 is positive, the parabola opens up so we have a minimum.

The vertex is  halfway between the x intercepts

(-4+2)/2 = -2/2 = -1

To find the minimum substitute x= -1 into the equation

f(x)=x^2+2x-8

f(-1) = (-1)^2 +2(-1)-8 = 1-2-8 = -9

The minimum is -9