Complete the Square Flashcard #4

Front

What is the formula to complete the square for a quadratic expression?

Back

To complete the square for a quadratic expression of the form ax^2 + bx + c, use the formula: (b/2a)^2.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

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

Front

What is the significance of the vertex in a parabola?

Back

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

Front

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

Back

To convert from standard form y = ax^2 + bx + c to vertex form, complete the square.

Front

What is the value that completes the square for the expression x^2 + 10x?

Back

The value that completes the square is 25.

Front

What is the vertex of the parabola given by y = x^2 - 2x + 4?

Back

The vertex of the parabola is (1, 3).

Front

How do you determine if a parabola opens upwards or downwards?

Back

A parabola opens upwards if the coefficient of x^2 (a) is positive, and downwards if a is negative.

Front

What is the axis of symmetry for a parabola in standard form?

Back

The axis of symmetry for a parabola in standard form y = ax^2 + bx + c is the vertical line x = -b/(2a).

Front

What is the process to convert y = 3x^2 + 6x - 5 to vertex form?

Back

1. Factor out the coefficient of x^2 from the first two terms. 2. Complete the square. 3. Rewrite in vertex form.