Completing the Square

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form of (x - p)^2 = q, where p and q are constants. This method helps to find the vertex form of the equation.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of a parabola given in standard form?

Back

For a quadratic function in standard form f(x) = ax^2 + bx + c, the vertex can be found using the formula h = -b/(2a) and k = f(h).

Front

Convert the quadratic equation f(x) = x^2 + 4x + 9 into vertex form.

Back

f(x) = (x + 2)^2 + 5.

Front

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

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens (upward or downward).

Front

How do you solve a quadratic equation by completing the square?

Back

1. Move the constant term to the other side. 2. Take half of the coefficient of x, square it, and add it to both sides. 3. Factor the left side and solve for x.

Front

What is the formula for the vertex of a parabola given by the equation y = ax^2 + bx + c?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).

Front

Convert the equation y = x^2 + 5x + 3 into vertex form.

Back

y = (x + 5/2)^2 - 13/4.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by D = b^2 - 4ac. It determines the nature of the roots.

Front

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

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).