Review for Quadratics Flashcard (OPTIONAL)

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c

Front

How do you find the maximum height of a projectile given the height function h = -16t² + 64t + 960?

Back

Set the derivative of h with respect to t to zero and solve for t. The maximum height occurs at t = 2 seconds.

Front

What does the vertex of a parabola represent?

Back

The vertex represents the maximum or minimum point of the parabola.

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 images, given by x = -b/(2a) for the equation y = ax² + bx + c.

Front

What does the term 'roots' refer to in a quadratic equation?

Back

Roots are the values of x where the quadratic function intersects the x-axis (where y = 0).

Front

What transformation occurs in the function y = (x - 3)²?

Back

The graph is translated right 3 units.

Front

What is the significance of the coefficient 'a' in the quadratic equation y = ax² + bx + c?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the formula to find the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What is the maximum point on a parabola called?

Back

The maximum point is called the vertex if the parabola opens downwards.