Shifting Parabolas

Front

What is the equation of the graph that opens upwards and has its vertex at (1, -5)?

Back

f(x) = (x - 1)² - 5

Front

If f(x) = x², what is the equation of the graph that is shifted 3 units to the right?

Back

g(x) = (x - 3)²

Front

What is the axis of symmetry for a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola.

Front

What is the vertex of the quadratic equation y = 2(x + 2)² + 5?

Back

The vertex is (-2, 5).

Front

What transformation occurs when the graph of y = x² is changed to y = x² + 8?

Back

The graph is shifted up 8 units.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

Front

How do you find the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What does the 'a' value in the quadratic equation y = ax² + bx + c 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.

Front

What is the effect of changing the 'c' value in the equation y = x² + c?

Back

Changing the 'c' value shifts the graph up or down without affecting its shape.

Front

What is the formula for the axis of symmetry of a parabola in vertex form y = a(x - h)² + k?

Back

The axis of symmetry is x = h.