Vertex Form Quadratics

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you determine if a parabola opens up or down?

Back

A parabola opens up if the coefficient 'a' in the vertex form f(x) = a(x-h)² + k is positive, and it opens down if 'a' is negative.

Front

What is the axis of symmetry 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

If a parabola has a vertex at (h, k), what is the equation of its axis of symmetry?

Back

The equation of the axis of symmetry is x = h.

Front

What does the vertex of a parabola represent?

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

How can you find the vertex from the standard form of a quadratic equation?

Back

To find the vertex from the standard form ax² + bx + c, use the formula h = -b/(2a) and then substitute h back into the equation to find k.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis, found by setting f(x) = 0 and solving for x.

Front

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

Back

The 'a' value determines the width and direction of the parabola; larger absolute values of 'a' make the parabola narrower.

Front

What is the relationship between the vertex and the y-intercept in a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, which can be found by evaluating f(0) in the vertex form.

Front

How do you graph a quadratic function in vertex form?

Back

To graph a quadratic function in vertex form, plot the vertex, draw the axis of symmetry, and then plot additional points on either side of the vertex.