Vertex Form

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

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

Back

The 'a' value determines the direction and width 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

How do you find the vertex from the vertex form equation?

Back

The vertex can be found directly from the vertex form f(x) = a(x - h)² + k as the point (h, k).

Front

What is the significance of the vertex in a parabola?

Back

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

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.

Front

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

Back

If 'a' in the vertex form is positive, the parabola has a minimum value at the vertex. If 'a' is negative, it has a maximum value.

Front

What is the relationship between the vertex and the axis of symmetry?

Back

The axis of symmetry always passes through the vertex of the parabola.

Front

How can you convert standard form to vertex form?

Back

You can convert standard form (f(x) = ax² + bx + c) to vertex form by completing the square.

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, found by evaluating f(0).