Solving quadratics by graphing practice

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 x-intercepts of a graph?

Back

The x-intercepts of a graph are the points where the graph crosses the x-axis, meaning the values of x for which y = 0.

Front

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

Back

To find the x-intercepts, set the quadratic equation equal to zero and solve for x.

Front

What does it mean to solve a quadratic equation by graphing?

Back

Solving a quadratic equation by graphing involves plotting the equation on a coordinate plane and identifying 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 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 is the quadratic formula?

Back

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

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

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

How can you determine the number of solutions from a graph?

Back

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