Vertex Form of Quadratics

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 identify the vertex from the vertex form of a quadratic equation?

Back

In the vertex form y = a(x - h)² + k, the vertex is the point (h, k).

Front

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

Back

The parameter 'a' indicates the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. The larger the absolute value of 'a', the narrower the parabola.

Front

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

Back

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

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 is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves. It is given by the equation x = h, where (h, k) is the vertex.

Front

How do you find the y-intercept of a quadratic equation in vertex form?

Back

To find the y-intercept of a quadratic equation in vertex form y = a(x - h)² + k, set x = 0 and solve for y.

Front

What is the effect of changing the value of 'h' in the vertex form of a quadratic?

Back

Changing the value of 'h' shifts the parabola horizontally. If 'h' increases, the parabola shifts to the right; if 'h' decreases, it shifts to the left.

Front

What is the effect of changing the value of 'k' in the vertex form of a quadratic?

Back

Changing the value of 'k' shifts the parabola vertically. If 'k' increases, the parabola shifts upwards; if 'k' decreases, it shifts downwards.

Front

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

Back

A quadratic function has a maximum value if 'a' is negative (the parabola opens downwards) and a minimum value if 'a' is positive (the parabola opens upwards).