How do you graph y=−2(3+x)2+4?

1 Answer
Ernest Z.
Aug 6, 2015

Calculate the vertex and the x- and y-intercepts and then sketch the graph.

Explanation:

y=−2(3+x)2+4

Step 1. Convert your equation to vertex form.

The vertex form is y=a(x−h)2+k.

Rearrange your equation to y=−2(x+3)2+4.

Then a=−2, h=−3, and k=4.

Step 2. Find the vertex.

The vertex is at (h,k) or (−3,4).

Step 3. Find the y-intercept.

Set x=0 and solve for y.

y=−2(3+x)2+4=−2(3)2+4=−2(9)+4=−18+4=−14

The y-intercept is at (0,−14).

Step 4. Find the x-intercept(s).

Set y=0 and solve for x.

0=−2(3+x)2+4

(3+x)2−2=0

((3+x)+√2)((3+x)−√2)=0

3+x+√2=0 and 3+x−√2=0

x=−3−√2≈−4.4 and x=−3+√2≈−1.6

Step 5. Draw your axes and plot the four points.

Graph 1Graph 1

Step 6. Draw a smooth parabola that passes through the four points.

Graph 2Graph 2

And you have your graph.

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