Quadratic Functions

Front

What is the equation for the axis of symmetry of a quadratic function?

Back

x = -b/(2a), where a and b are coefficients from the quadratic equation ax² + bx + c.

Front

Identify the vertex of the quadratic function y = ax² + bx + c.

Back

The vertex is given by the point (h, k) where h = -b/(2a) and k = f(h).

Front

What does it mean if a quadratic function opens upwards?

Back

The leading coefficient (a) is positive, and the vertex represents the minimum point of the graph.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a quadratic function opens downwards?

Back

The leading coefficient (a) is negative, and the vertex represents the maximum point of the graph.

Tags

CCSS.HSF-IF.C.7A

Front

How do you find the roots of a quadratic equation?

Back

Use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

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 downwards?

Back

All real numbers less than or equal to the y-coordinate of the vertex.

Front

Solve the quadratic equation: a² + 2a - 24 = 0.

Back

a = -6, 4.

Tags

CCSS.HSA-REI.B.4B

Front

What is the maximum or minimum value of the quadratic function y = -4x² + 8x + 1?

Back

Maximum value, since the leading coefficient is negative.

Front

What is the standard form of a quadratic function?

Back

y = ax² + bx + c.