Quadratics in Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

Front

How do you find the value of 'c' to complete the square for the expression x^2 - 8x + ___?

Back

To complete the square, take half of the coefficient of x (which is -8), square it, and add it. So, c = (-8/2)^2 = 16.

Front

What does the 'h' value represent in the vertex form of a quadratic equation?

Back

The 'h' value represents the x-coordinate of the vertex of the parabola.

Front

What does the 'k' value represent in the vertex form of a quadratic equation?

Back

The 'k' value represents the y-coordinate of the vertex of the parabola.

Front

How does the value of 'a' affect the graph of a quadratic function in vertex form?

Back

If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. The larger the absolute value of 'a', the steeper the parabola.

Front

What is the effect of translating the graph of y = (x - 3)^2 + 2?

Back

The graph is translated right 3 units and up 2 units.

Front

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

Back

If 'a' (the coefficient of the squared term) is positive, the function has a minimum value. If 'a' is negative, it has a maximum value.

Front

What is the axis of symmetry for the quadratic function y = (x + 4)^2 - 1?

Back

The axis of symmetry is the vertical line x = -4.

Front

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

Back

To convert, complete the square on the quadratic expression.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function, depending on whether it opens upwards or downwards.