Quadratic Features & Transformations

Front

What is a parabola?

Back

A parabola is a symmetrical, curved shape that represents the graph of a quadratic function, typically in the form y = ax² + bx + c.

Front

How many zeros can a parabola have?

Back

A parabola can have 0, 1, or 2 zeros (x-intercepts), depending on its position relative to the x-axis.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of a parabola, depending on whether it opens upwards or downwards.

Front

What does the 'a' value in a quadratic function affect?

Back

The 'a' value affects the width and direction of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

What transformation occurs when you add a constant to a quadratic function?

Back

Adding a constant to a quadratic function results in a vertical translation of the graph.

Front

What transformation occurs when you replace x with (x - k) in a quadratic function?

Back

Replacing x with (x - k) results in a horizontal translation of the graph k units to the right.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the factored form of a quadratic function?

Back

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

Front

What is the quadratic formula?

Back

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