Characteristics of Quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' determine in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upward or downward.

Front

How do you find the vertex of a quadratic function in vertex form?

Back

In vertex form, y = a(x - h)² + k, the vertex is the point (h, k).

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 = h, where (h, k) is the vertex.

Front

What is the range of a quadratic function that opens upward?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.

Tags

CCSS.HSF-IF.C.7A

Front

What is the range of a quadratic function that opens downward?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.

Tags

CCSS.HSF-IF.C.7A

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

What is the factored form of a quadratic function?

Back

The factored form is y = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots of the quadratic.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

How do you find the roots of a quadratic equation?

Back

You can find the roots using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B