What is the vertex of the parabola y=−x2−2x+3?

1 Answer
Daft
Mar 16, 2017

(−1,4)

Explanation:

There is a lovely and straightforward (which makes it all the lovelier) rule for working out vertices such as this one.

Think of the general parabola: y=ax2+bx+c, where a≠0

The formula for finding the x-vertex is −b2a and to find the y-vertex, you insert the value you found for x into the formula.

Using your question y=−x2−2x+3 we can establish the values of a,b,and c.

In this case:

a=−1
b=−2; and
c=3.

To find the x-vertex we need to replace the values for a and b in the formula given above (−b2a):

=−(−2)2⋅(−1)=2−2=−1

So we now know that the x-vertex is at −1.

To find the y-vertex, go back to the original question and replace all the instances of x with −1:

y=−x2−2x+3

y=−(−1)2−2⋅(−1)+3

y=−1+2+3

y=4

We now know that the x-vertex is at −1 and the y-vertex is at 4 and this can be written in coordinate format:

(−1,4)

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