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 no real solutions?

Back

It means that the graph of the quadratic does not intersect the x-axis, indicating that the solutions are complex numbers.

Front

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

Back

By observing the number of times the graph intersects the x-axis: 0 intersections means no real solutions, 1 intersection means one real solution, and 2 intersections mean two real solutions.

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x that make the quadratic equation equal to zero; they are the x-intercepts of the graph.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function, depending on the direction of the parabola.

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 significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of the function when x = 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form is written as y = ax² + bx + c.

Front

What is the factored form of a quadratic equation?

Back

The factored form is written as y = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Front

How do you find the x-intercepts of a quadratic function?

Back

Set the quadratic equation equal to zero and solve for x.