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

How can you determine if a parabola opens upwards or downwards?

Back

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

Front

What does the vertex of a parabola represent?

Back

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

Front

How do you find the maximum or minimum value of a parabola in vertex form?

Back

The maximum or minimum value of a parabola in vertex form y = a(x - h)² + k is the value of k. If 'a' is negative, k is the maximum; if 'a' is positive, k is the minimum.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts (or roots) of a parabola are the points where the graph intersects the x-axis, found by setting y = 0 and solving for x.

Front

How do you convert standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form y = a(x - h)² + k, you can complete the square.

Front

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

Back

The 'h' value in the vertex form y = a(x - h)² + k indicates the x-coordinate of the vertex and the axis of symmetry of the parabola.

Front

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

Back

The 'k' value in the vertex form y = a(x - h)² + k indicates the y-coordinate of the vertex and the maximum or minimum value of the parabola.

Front

If a parabola has a vertex at (2, -3), what is its vertex form?

Back

The vertex form of the parabola is y = a(x - 2)² - 3, where 'a' determines the direction and width of the parabola.

Front

How do you find the axis of symmetry of a parabola in vertex form?

Back

The axis of symmetry of a parabola in vertex form y = a(x - h)² + k is the vertical line x = h.