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 standard forms of a quadratic equation?

Back

The standard form is y = ax² + bx + c, and the factored form is y = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots.

Front

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

Back

Solving a quadratic equation by graphing involves plotting the quadratic function on a coordinate plane and identifying the x-intercepts, which represent the solutions.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, corresponding to the solutions of the equation.

Front

How can you find the vertex of a quadratic function?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)), where f(x) is the quadratic function.

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 equation x = -b/2a.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by D = b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution, also known as a repeated or double root.

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.