Graphing Parabolas Math Example 2

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Example 2

medium
Sketch g(x)=−x2+2x+3g(x) = -x^2 + 2x + 3. Find vertex and intercepts.

Solution

  1. 1
    Direction: a=−1<0a = -1 < 0, opens downward.
  2. 2
    Vertex: x=−22(−1)=1x = -\frac{2}{2(-1)} = 1; g(1)=−1+2+3=4g(1) = -1 + 2 + 3 = 4. Vertex: (1,4)(1, 4).
  3. 3
    yy-intercept: g(0)=3g(0) = 3.
  4. 4
    xx-intercepts: −x2+2x+3=0⇒x2−2x−3=0⇒(x−3)(x+1)=0-x^2 + 2x + 3 = 0 \Rightarrow x^2 - 2x - 3 = 0 \Rightarrow (x-3)(x+1) = 0, so x=3,−1x = 3, -1.

Answer

Vertex (1,4)(1,4), opens down, xx-intercepts at −1-1 and 33.
A negative leading coefficient means the parabola opens downward and the vertex is a maximum point.

About Graphing Parabolas

The process of plotting a quadratic function by identifying its key features: vertex, axis of symmetry, direction of opening, yy-intercept, and xx-intercepts (if they exist).

Learn more about Graphing Parabolas →

More Graphing Parabolas Examples

Example 1 easy

Identify the key features of [formula] for graphing.

Example 3 easy

Does [formula] have any [formula]-intercepts?

Example 4 medium

The vertex of a parabola is [formula] and it passes through [formula]. Find the equation.

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