9-2a-Solving Quadratic Equations by Graphing

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean for a quadratic equation to have 0 solutions?

Back

A quadratic equation has 0 solutions when its graph does not intersect the x-axis, indicating that there are no real roots.

Front

How do you determine the number of solutions of a quadratic equation by graphing?

Back

The number of solutions can be determined by the number of times the graph of the quadratic function intersects the x-axis.

Front

What are the roots of a quadratic function?

Back

The roots of a quadratic function are the x-values where the function equals zero, or where the graph intersects the x-axis.

Front

If a quadratic function has roots at x = 0 and x = 4, what are the solutions?

Back

The solutions are x = 0 and x = 4.

Front

What does it mean for a quadratic equation to have 1 solution?

Back

A quadratic equation has 1 solution when its graph is tangent to the x-axis, meaning it touches the x-axis at one point.

Front

How can you use a graph to solve a quadratic equation?

Back

You can solve a quadratic equation by finding the x-values where the graph intersects the x-axis.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on its orientation.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.