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?

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

What is the axis of symmetry for a quadratic in vertex form?

Back

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

Front

How does the vertex form relate to the standard form of a quadratic equation?

Back

The vertex form y = a(x - h)² + k can be converted to standard form y = ax² + bx + c by expanding the equation.

Front

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

Back

Changing 'h' in the vertex form y = a(x - h)² + k translates the graph horizontally. If 'h' increases, the graph shifts to the right; if 'h' decreases, it shifts to the left.

Front

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

Back

Changing 'k' in the vertex form y = a(x - h)² + k translates the graph vertically. If 'k' increases, the graph shifts upward; if 'k' decreases, it shifts downward.

Front

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

Back

You can determine the direction of opening of a parabola from its vertex form by looking at the value of 'a'. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What does the vertex represent in the context of a quadratic function?

Back

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

Front

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

Back

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