Completing The Square Practice

Front

What is the vertex of the quadratic equation in vertex form?

Back

The vertex of the quadratic equation y = a(x-h)^2 + k is (h, k).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

How do you complete the square for the expression x^2 + bx?

Back

To complete the square, take half of b, square it, and add it to the expression: x^2 + bx + (b/2)^2.

Front

What is the value of 'c' that completes the square in the expression x^2 + 28x + c?

Back

The value of 'c' is 196, since (28/2)^2 = 196.

Front

What are the roots of the equation n^2 - 14n - 76 = -4?

Back

The roots are n = 18 and n = -4.

Front

What is the quadratic formula used to find the roots of a quadratic equation?

Back

The quadratic formula is n = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.

Front

How can you identify the axis of symmetry for a quadratic function?

Back

The axis of symmetry for the quadratic function y = ax^2 + bx + c is x = -b/(2a).

Front

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

Back

The vertex represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

Front

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

Back

To convert, complete the square on the quadratic expression.