Math 3 wk 1

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the value of c in a quadratic function given the vertex?

Back

To find the value of c in a quadratic function of the form y = ax^2 + bx + c, substitute the x-coordinate of the vertex into the equation and set y equal to the y-coordinate of the vertex.

Front

What is the complete factorization of a quadratic expression?

Back

The complete factorization of a quadratic expression is the expression written as a product of its linear factors.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

A quadratic opens upwards if the coefficient a is positive and downwards if a is negative.

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 the formula x = -b/(2a).

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the vertex form of a quadratic function?

Back

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

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.