Solving Quadratics 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 to be solved by graphing?

Back

Solving a quadratic by graphing involves plotting the quadratic function on a coordinate plane and identifying the points where the graph intersects the x-axis, which represent the solutions (or roots) of the equation.

Front

What are the x-intercepts of a graph?

Back

The x-intercepts of a graph are the points where the graph crosses the x-axis, which occur when y = 0.

Front

How do you find the roots of a quadratic equation graphically?

Back

To find the roots graphically, plot the quadratic function and look for the x-values where the graph intersects the x-axis.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola (opening upwards or downwards).

Front

What is the axis of symmetry in a quadratic graph?

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 significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What are the steps to graph a quadratic function?

Back

1. Identify the vertex. 2. Determine the axis of symmetry. 3. Find the x-intercepts (roots). 4. Plot additional points if necessary. 5. Draw the parabola.

Front

What is a zero of a function?

Back

A zero of a function is a value of x that makes the function equal to zero, corresponding to the x-intercepts of the graph.

Front

How can you verify the solutions of a quadratic equation?

Back

You can verify the solutions by substituting them back into the original equation to see if they satisfy it.