Solving Quadratic Equations: Graphs and Tables

When using a graph to solve a quadratic equation, the solutions are found at which of the following points?

• The vertex of the parabola.

• The y-intercepts of the graph.

• The x-intercepts of the graph.

• The maximum points of the graph.

Answer explanation

The solutions to a quadratic equation are found at the x-intercepts of the graph, where the equation crosses the x-axis.

How many solutions can you find for a quadratic equation by identifying the x-intercepts on a graph?

• Always 1

• Always 2

• 0, 1, or 2

• Always 0

Answer explanation

Identifying x-intercepts on a graph of a quadratic equation can yield 0, 1, or 2 solutions, depending on the position of the intercepts relative to the x-axis.

What does it mean if a quadratic graph does not touch or cross the x-axis?

• The quadratic equation has no real solutions.

• The quadratic equation has exactly one real solution.

• The quadratic equation has two real solutions.

• The quadratic equation cannot be solved graphically.

Answer explanation

If a quadratic graph does not touch or cross the x-axis, it means the quadratic equation has no real solutions.

Answer explanation

The y values first increase, then decrease, forming a parabolic shape typical of a quadratic equation.