QUADRATIC GRAPHS

Front

What is the standard form of a quadratic function?

Back

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

Front

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

Back

The 'a' value 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).

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 upward or downward.

Front

How do you find the vertex of a parabola given in vertex form y = a(x - h)^2 + k?

Back

The vertex is given by the point (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 = -b/(2a).

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

What transformation occurs when a quadratic function is reflected over the x-axis?

Back

The graph of the function is inverted, changing the direction of the parabola.

Front

What does a vertical stretch by a factor of 'k' do to the graph of a quadratic function?

Back

It makes the parabola narrower if k > 1 and wider if 0 < k < 1.

Front

What is the maximum value of a quadratic function that opens downward?

Back

The maximum value is the y-coordinate of the vertex.

Front

What is the minimum value of a quadratic function that opens upward?

Back

The minimum value is the y-coordinate of the vertex.