Quadratics Domain and Range

Front

What is the domain of a quadratic function?

Back

All Real Numbers

Front

What is the range of the function y = x^2?

Back

[0, inf) because the minimum value is 0.

Front

What is the range of the function y = -x^2 + 4?

Back

(-inf, 4] because the maximum value is 4.

Front

What does it mean for a parabola to open upwards?

Back

The vertex is the minimum point, and the range is [k, inf) where k is the y-coordinate of the vertex.

Front

What does it mean for a parabola to open downwards?

Back

The vertex is the maximum point, and the range is (-inf, k] where k is the y-coordinate of the vertex.

Front

What is a maximum point on a parabola?

Back

The highest point on the graph of a downward-opening parabola.

Front

What is a minimum point on a parabola?

Back

The lowest point on the graph of an upward-opening parabola.

Front

What are the roots of a quadratic function?

Back

The x-values where the function intersects the x-axis (y=0).

Front

How do you find the vertex of a quadratic function in standard form y = ax^2 + bx + c?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the vertex of the function y = 2x^2 - 8x + 6?

Back

(2, -2) because x = -(-8)/(2*2) = 2 and y = 2(2)^2 - 8(2) + 6 = -2.