Key features of a Parabola

Front

Define Vertex

Back

The highest or lowest point on the graph.

Front

What is the Axis of Symmetry?

Back

A line that divides the graph into two equal parts, cutting the graph in half.

Front

Identify the y-intercept of a parabola.

Back

The point where the graph intersects the y-axis.

Front

What are x-intercepts?

Back

The points where the graph intersects the x-axis.

Front

What is the standard form of a quadratic function?

Back

f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

It determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What is the significance of the discriminant in a quadratic equation?

Back

It determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you find the vertex of a parabola in standard form?

Back

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

Front

What is the range of a parabola that opens upwards?

Back

The range is from the vertex's y-coordinate to positive infinity.

Front

What is the domain of a parabola?

Back

The domain of a parabola is all real numbers.