Question

Find the vertex of the quadratic function f(x)=x^2-6x+1

Answer 1

(3, 8).

Explanation:

1. Write the expression in general form.

General form is: y = ax² + bx + c.

`y=x^2-6x+1`

2. Use the following formula to find the "x" coordinate of the vertex.

Formula:
`x=-(b)/(2a)`

3. Identify "b" and "a" from the general form.

So "b" should be the coefficient of the "x" variable, that value is: -6.

Now, the "a" value is implicit, since the x² doesn't have any numbers in front of it. Therefore, the value of "a" is 1.

4. Use the values to calculate the "x" coordinate of the vertex.

`x=-(((-6))/(2(1)))\\ \\x=-((-6)/(2))\\ \\x=-(-3)\\ \\x=3`

5. Substitute "x" by the calculated value (3) in the original function formula to find the "y" coordinate of the vertex.

`y=x^2-6x+1\\ \\y=(3)^2-6(3)+1\\ \\y=9-18+1\\ \\y=-8`

6. Write the ordered pair of the vertex.

(3, 8).

7. Graph.

Take a look at the attached image to see the graph and vertex of this function.