Flashcard - Forms of Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax² + bx + c.

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

How do you find the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, f(0)).

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for a parabola to have a minimum?

Back

A parabola has a minimum if it opens upwards, meaning the vertex is the lowest point on the graph.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean for a parabola to have a maximum?

Back

A parabola has a maximum if it opens downwards, meaning the vertex is the highest point on the graph.

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine the zeros of a quadratic function?

Back

The zeros of a quadratic function can be found by setting the function equal to zero and solving for x, either by factoring, using the quadratic formula, or completing the square.

Tags

CCSS.HSF-IF.C.7C

Front

What is the quadratic formula?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry of a parabola is a vertical line that passes through the vertex, dividing the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

Front

What are the characteristics of the graph of a quadratic function?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards, has a vertex, an axis of symmetry, and may intersect the x-axis at zero, one, or two points.

Tags

CCSS.HSF-IF.C.7A