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 find the vertex of a parabola given in vertex form?

Back

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

Front

What does the 'a' value in the vertex form indicate about the parabola?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its width (larger |a| means narrower, smaller |a| means wider).

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the x-values where the function intersects the x-axis, also known as the roots.

Front

How can you find the zeros of a quadratic function in vertex form?

Back

To find the zeros, set f(x) = 0 and solve for x: 0 = a(x-h)² + k.

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, given by the equation x = h.

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the parabola opens upward and has a minimum value at the vertex. If 'a' is negative, it opens downward and has a maximum value at the vertex.

Front

What is the significance of the vertex in a quadratic function?

Back

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

Front

How can you convert a quadratic function from standard form to vertex form?

Back

You can convert by completing the square on the standard form equation.

Front

What is the relationship between the vertex and the maximum/minimum value of a quadratic function?

Back

The y-coordinate of the vertex gives the maximum or minimum value of the function.