Quadratic Translations

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the vertex of a quadratic function?

Back

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

Front

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

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

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 formula x = -b/(2a).

Front

How does the 'h' value in vertex form affect the graph of a quadratic function?

Back

The 'h' value in vertex form y = a(x - h)² + k shifts the graph horizontally. If h is positive, the graph shifts to the right; if negative, to the left.

Front

How does the 'k' value in vertex form affect the graph of a quadratic function?

Back

The 'k' value in vertex form y = a(x - h)² + k shifts the graph vertically. If k is positive, the graph shifts up; if negative, down.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x².

Front

What transformation does the equation y = (x - 3)² represent?

Back

This equation represents a horizontal shift of the parent function 3 units to the right.

Front

What transformation does the equation y = (x + 2)² - 5 represent?

Back

This equation represents a horizontal shift 2 units to the left and a vertical shift down 5 units.

Front

What is the effect of adding a constant outside the quadratic function?

Back

Adding a constant outside the function shifts the graph vertically. For example, y = x² + 3 shifts the graph up 3 units.