Section 6.1 (Day 1)

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point (h, k) where the function reaches its maximum or minimum value, given by the formula h = -b/(2a) and k = f(h).

Front

What does the 'a' value in a quadratic function indicate?

Back

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

Front

How do you find the vertex from the standard form of a quadratic function?

Back

To find the vertex from the standard form f(x) = a(x-h)² + k, the vertex is simply (h, k).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h, where (h, k) is the vertex.

Front

What transformation does the equation g(x) = f(x) - 5 represent?

Back

This represents a vertical shift downward by 5 units.

Front

What transformation does the equation g(x) = f(x + 3) represent?

Back

This represents a horizontal shift to the left by 3 units.

Front

What is the effect of a negative 'a' value in a quadratic function?

Back

A negative 'a' value reflects the parabola over the x-axis, making it open downward.

Front

How do you determine if a quadratic function opens upward or downward?

Back

If the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

What is a vertical stretch in a quadratic function?

Back

A vertical stretch occurs when the absolute value of 'a' is greater than 1, making the parabola narrower.