Question

Graph y=X^2-3x+4. Find the axis of symmetry and the vertex

Answer 1

The coordinates of the vertex are (1.5, 1.75) and the axis of symmetry is at x = 1.5.

We can find the vertex by using the formula for finding x-coordinates. The formula for the x-coordinate of a vertex is below.

-b/2a

In this equation, a is the coefficient of the x^2 term (1) and b is the coefficient of the x term (-3). Then we can plug in to find the x term.

-(-3)/2(1)

3/2

1.5

Now that we have this term, we can plug it in for all values of x to find the y term.

x^2 - 3x + 4

1.5^2 - 3(1.5) + 4

2.25 - 4.5 + 4

1.75

Now we know that the vertex is at (1.5, 1.75). Now finding the axis of symmetry is easy because the axis of symmetry in any quadratic is simply x = [x-coordinate of vertex]. So in this case it would be x = 1.5.