What is the axis of symmetry and vertex for the graph y = 2x^2 - 2x + 5?

1 Answer
Akazukin 赤ずきん
Nov 6, 2017

Vertex: (0.5,4.5)
Axis of Symmetry: x = 0.5

Explanation:

First, we have to convert y=2x^2 - 2x + 5 into vertex form, because it is currently in standard form (ax^2 + bx + c). To do this, we must complete the square and find the perfect square trinomial that corresponds with the equation.

First, factor the 2 out of our first two terms: 2x^2 and x^2.

This becomes 2(x^2 - x) + 5.

Now, use x^2-x to complete the square, adding and subtracting (b/2)^2.

Since there is no coefficient in front of x, we can assume that it is -1 because of the sign.

([-1]/2)^2 = 0.25

2(x^2-x+0.25-0.25)+5

Now, we can write this as a binomial squared.

2[(x - 0.5)^2-0.25] + 5

We must multiply the -0.25 by 2 to get rid of its brackets.

This becomes 2(x-0.5)^2-0.5+5

Which simplifies to 2(x-0.5)^2+4.5

It's finally in vertex form! We can easily see that the vertex is (0.5,4.5), and the axis of symmetry is simply the x coordinate of the vertex.

Vertex: (0.5,4.5)
Axis of Symmetry: x = 0.5

Hope this helps!

Best wishes,
A fellow highschool student

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