Solving Quadratics by Graphing

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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, meaning the value of y is 0 at these points.

Front

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

Back

To find the x-intercepts of a quadratic function, set the function equal to zero (y = 0) and solve for x.

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 function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What does it mean for a number to be a zero of a function?

Back

A zero of a function is a value of x that makes the function equal to zero (f(x) = 0). It corresponds to the x-intercepts of the graph.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What is the factored form of a quadratic equation?

Back

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

Front

How can you determine the number of real roots of a quadratic function?

Back

The number of real roots can be determined using the discriminant (D = b² - 4ac). If D > 0, there are 2 real roots; D = 0 means 1 real root; D < 0 means no real roots.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.