Writing Quadratics in Vertex Form

Front

What is the vertex of a parabola in vertex form?

Back

The vertex of a parabola in vertex form y = a(x - h)² + k is the point (h, k).

Front

What does the axis of symmetry represent in a parabola?

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 identify the vertex from the equation y = a(x - h)² + k?

Back

The vertex is the point (h, k) where the parabola reaches its maximum or minimum value.

Front

Convert the equation y = 2x² + 8x + 6 into vertex form.

Back

y = 2(x + 2)² - 2.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

How do you convert from standard form to vertex form?

Back

To convert, complete the square on the quadratic expression.

Front

What is the significance of the 'a' value in the vertex form of a parabola?

Back

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

Front

Given the equation y = -3(x - 1)² + 5, what is the vertex?

Back

The vertex is (1, 5).

Front

What is the effect of changing the 'h' value in vertex form?

Back

Changing 'h' shifts the parabola left or right along the x-axis.

Front

What is the effect of changing the 'k' value in vertex form?

Back

Changing 'k' shifts the parabola up or down along the y-axis.