What is the y-coordinate of the vertex of a parabola with the following equation #y = x^2 - 8x + 18#?
1 Answer
Vertex = (4,2)
Explanation:
To find the vertex of a quadratic equation you can either use use the vertex formula or put the quadratic in vertex form:
Method 1: Vertex formula
a is the coefficient of the first term in the quadratic, b is the coefficient of the second term and c is the coefficient of the third term in the quadratic.
In this case a = 1 and b = -8, so substituting these values into the formula above gives:
which becomes:
which simplifies to:
Method 2: Vertex form
vertex form looks like this:
To convert from quadratic form to vertex form substitute the variables in the next equation with the coefficients of the quadratic
In this case b = -8 and c = 18
Substituting these variables we get
Which becomes:
which simplifies to:
This is called the vertex form because the vertex can be easily found in this form.
Note: This method can be quicker than the first method but only works when the coefficient of a is 1.