Week 16 Flashcard Graphing Quadratics in Vertex Form

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

How do you find the axis of symmetry from a quadratic equation in vertex form?

Back

For a quadratic equation in the form y = a(x - h)² + k, the axis of symmetry is the line x = h.

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 upwards or downwards.

Front

Given the equation y = 2(x - 5) + 6, what is the vertex?

Back

The vertex is (5, 6).

Front

What does the term 'vertex form' refer to in quadratic equations?

Back

Vertex form is a way of expressing a quadratic function as y = a(x - h)² + k, where (h, k) is the vertex.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you convert from vertex form to standard form?

Back

Expand the equation y = a(x - h)² + k to get y = ax² - 2ahx + (ah² + k).

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the factored form of a quadratic equation?

Back

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

Front

How do you find the roots of a quadratic equation?

Back

You can find the roots by factoring, using the quadratic formula, or completing the square.