# What is the equation of the parabola that has a vertex at # (-1, 16) # and passes through point # (3,20) #?

##### 2 Answers

#### Explanation:

The standard form of the equation of a parabola is:

From the question we know two things.

- The parabola has a vertex at
#(-1, 16)# - The parabola passes through the point
#(3, 20)#

With those two pieces of information, we can construct our equation for the parabola.

Let's start off with the basic equation:

Now we can substitute our vertex coordinates for

The

Note that putting

Now substitute the point the parabola passes through for

Looks good. Now we have to find

Combine all like terms:

Add 3 + 1 inside the parentheses:

Square 4:

Factor out 16:

Divide both sides by 16:

Simplify

Subtract 1 from both sides:

The LCD of 4 and 1 is 4 so

Subtract:

Switch sides if you want:

Now that you've found

And that's your equation.

Hope this helped.

#### Explanation:

#"the equation of a parabola in "color(blue)"vertex form"# is.

#color(red)(bar(ul(|color(white)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

#"where "(h,k)" are the coordinates of the vertex and a"#

#"is a multiplier"#

#"here "(h,k)=(-1,16)#

#rArry=a(x+1)^2+16#

#"to find a substitute "(3,20)" into the equation"#

#20=16a+16rArra=1/4#

#rArry=1/4(x+1)^2+16larrcolor(red)"in vertex form"#