Solve 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 are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero. They are also known as the roots or solutions of the equation.

Front

How do you find the zeros of a quadratic function by graphing?

Back

To find the zeros by graphing, plot the quadratic function on a coordinate plane and identify the points where the graph intersects the x-axis.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards if the coefficient of x² (a) is positive, resulting in a U-shaped graph.

Front

What does it mean for a quadratic function to open downwards?

Back

A quadratic function opens downwards if the coefficient of x² (a) is negative, resulting in an upside-down U-shaped graph.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Front

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

Back

The number of real solutions can be determined using the discriminant (b² - 4ac). If it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.