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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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.

Tags

CCSS.HSA-REI.B.4B