Solving 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 solutions of a quadratic equation?

Back

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

Front

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

Back

You can find the solutions by graphing the quadratic function and identifying the x-intercepts, where the graph crosses the x-axis.

Front

What does it mean for a quadratic equation to have real solutions?

Back

A quadratic equation has real solutions if the graph intersects the x-axis at one or two points.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a 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 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 do you determine the zeros of a quadratic function?

Back

The zeros can be determined by setting the quadratic function equal to zero and solving for x.

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.