(c) Sketch its graph.

Thank you for the opportunity to help you with your question!

The given quadratic equation is f(x) = 2x^2 + 6x

To find the standard form, factorize the equation as

x(2x+6)=0

Now, use the MPZ (Multiplication Property of Zero) to say that

x=0 or 2x+6=0

Which gives you two solutions:

x=0 or x=−3

To find the x-intercepts, we need to solve equation 2x^2+6x=0

y - intercept is point:Y(0,0)

To compute y - coordinate of y - intercept, we will find f(0). In this example we have:

f(0)=2⋅02+6⋅0+=0

Vertex is point: V=(−32,−92)

Explanation: to find the x - coordinate of the vertex we use formula

x=−b/2a

In this example: a=2,b=6,c=0. So, the x-coordinate of the vertex is:

x=−b/2a=−62⋅2=−32

f(−32)=2(−32)2+6⋅(−32)+0=−92

Focus is point: F=(−32,−358)

Explanation:

The x - coordinate of the focus is x=−b/2a

The y - coordinate of the focus is y=1−b^2/4a +C

Can you publish answers more clearly

Graph.docx

I am sending the word file. Kindly see...

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up