Guided Practice


Write the equation of the parabola in vertex form. The vertex is (−3, 3) and the parabola passes through the point (4, 150). Create a rough sketch of the graph to use as a visual aid.


A.
y = 3(x + 3)^2 + 3


B.
y = 4(x − 3)^2 + 3


C.
y = 50(x + 3)^2 + 4


D.
y = 3(x − 3)^2 + 3

Answer:

A.

y = 3(x + 3)^2 + 3

Step-by-step explanation:

The vertex form of the equation is y=a(x-h)2 + k  

You know that the vertex (h,k)  is (-3,3) and a point on the parabola is (4,150). So what you’re needed ing to find is a bc all of the other letters can be replaced into the equation.  

First I would put the equation into vertex form using the vertex given in the problem. : y= (x - (-3))2 + (3). Then I would use the ordered pair (4,150) and replace the x and y with those values

150 = a(4 + 3)2 + 3  

Now simplify

150 = a (7)2 + 3  

150 = 49a + 3      Important: please be sure to square.

147 = 49a

3= a  

Next replace a into the formula now leaving x and y alone.

y = 3 (x+3)2 + 3   [Vertex form]

I hope this helps. Have a great day!

Answer:

A.  [tex]y = 3(x + 3)^2 +3[/tex]

Step-by-step explanation:

The vertex form is:

[tex]y = a(x - h)^2 + k[/tex]

Where [tex]a[/tex] is the variable that determinate if the parabola is facing up or facing down and [tex]h[/tex] is the [tex]x[/tex] coordinate of the vertex and [tex]k[/tex] is the [tex]y[/tex] coordinate of the vertex.

So with the given values we have:

[tex]150 = a(4 + 3)^2 + 3[/tex]

Then isolate [tex]a[/tex] for find the missing value.

[tex]147 = a49\\\frac{147}{49} = a\\3 = a[/tex]

Then the final answer is [tex]y = 3(x + 3)^2 +3[/tex]

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