Math 3 wk 1

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = 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 its equation in standard form?

Back

To find the vertex of a parabola in standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic equation in the form y = a(x-h)² + k to easily identify the vertex.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: D > 0 means two real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = h in vertex form.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola; it is k in the vertex form y = a(x-h)² + k.

Front

What is the relationship between the coefficients and the graph of a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.