Quadratic Functions Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Find the vertex of f(x)=x2โˆ’6x+8f(x) = x^2 - 6x + 8.

Solution

  1. 1
    The xx-coordinate of the vertex is x=โˆ’b2a=โˆ’โˆ’62(1)=3x = -\frac{b}{2a} = -\frac{-6}{2(1)} = 3.
  2. 2
    The yy-coordinate is f(3)=9โˆ’18+8=โˆ’1f(3) = 9 - 18 + 8 = -1.
  3. 3
    The vertex is (3,โˆ’1)(3, -1).

Answer

(3,โˆ’1)(3, -1)
For a quadratic f(x)=ax2+bx+cf(x) = ax^2 + bx + c, the vertex formula x=โˆ’b2ax = -\frac{b}{2a} gives the axis of symmetry. Plugging this xx back in gives the minimum (if a>0a > 0) or maximum (if a<0a < 0) value.

About Quadratic Functions

A quadratic function is a polynomial function of degree 2, written as f(x)=ax2+bx+cf(x) = ax^2 + bx + c with aโ‰ 0a \neq 0, whose graph is a U-shaped curve called a parabola that opens upward when a>0a > 0 or downward when a<0a < 0.

Learn more about Quadratic Functions โ†’

More Quadratic Functions Examples

Example 2 medium

Does the parabola [formula] open upward or downward? Find its maximum value.

Example 3 medium

Find the vertex and axis of symmetry of [formula].

Example 4 easy

Find the [formula]-intercept of [formula].

Example 5 medium

Find the zeros of [formula].

โ† All Quadratic Functions Examples Quadratic Functions Concept