Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by y = 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 indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How do you find the vertex from the vertex form?

Back

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

Front

What are the roots of a quadratic equation?

Back

The roots (or solutions) of a quadratic equation are the x-values where the graph intersects the x-axis.

Front

How can you determine the y-intercept from the vertex form?

Back

To find the y-intercept, set x = 0 in the vertex form equation and solve for y.

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

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it indicates that the vertex is a maximum point, and the 'a' value in the vertex form is negative.

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 up or down.

Front

How do you convert standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form, complete the square.

Front

What is the formula to find the x-coordinate of the vertex from standard form?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a) from the standard form y = ax² + bx + c.