Graphing Parabolas Math Example 3

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

Example 3

easy
Does f(x)=5x2+1f(x) = 5x^2 + 1 have any xx-intercepts?

Solution

  1. 1
    Set 5x2+1=05x^2 + 1 = 0: x2=−15x^2 = -\frac{1}{5}.
  2. 2
    No real solution (can't square a real number to get negative). No xx-intercepts.

Answer

No xx-intercepts.
When the parabola's vertex is above the xx-axis and it opens upward, the parabola never crosses the xx-axis.

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 2 medium

Sketch [formula]. Find vertex and intercepts.

Example 4 medium

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

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