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 do you find the vertex from the vertex form equation y = a(x - h)² + k?

Back

The vertex is the point (h, k) in the equation.

Front

What does the 'a' in the vertex form y = a(x - h)² + k represent?

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 given in vertex form?

Back

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.

Front

If the vertex of a parabola is (-5, -4), what is the equation in vertex form?

Back

The equation is y = a(x + 5)² - 4, where 'a' can be any non-zero value.

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

How can you determine the direction of a parabola from its vertex form?

Back

By looking at the 'a' value: if 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.

Front

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

Back

The vertex lies on the axis of symmetry, which divides the parabola into two mirror-image halves.

Front

How do you convert the standard form of a quadratic equation to vertex form?

Back

You can use completing the square to convert from standard form ax² + bx + c to vertex form y = a(x - h)² + k.

Front

What is the formula for finding 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 ax² + bx + c.