Quadratic Functions Math Example 2

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

Example 2

medium
Does the parabola g(x)=โˆ’2x2+4x+1g(x) = -2x^2 + 4x + 1 open upward or downward? Find its maximum value.

Solution

  1. 1
    Since a=โˆ’2<0a = -2 < 0, the parabola opens downward.
  2. 2
    Vertex xx-coordinate: x=โˆ’42(โˆ’2)=1x = -\frac{4}{2(-2)} = 1.
  3. 3
    Maximum value: g(1)=โˆ’2(1)+4(1)+1=3g(1) = -2(1) + 4(1) + 1 = 3.
  4. 4
    The maximum value is 33 at x=1x = 1.

Answer

Opens downward; maximum value is 33.
The sign of aa determines the direction: a>0a > 0 opens upward (minimum), a<0a < 0 opens downward (maximum). The vertex gives the extreme 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 1 easy

Find the vertex of [formula].

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].

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