Parabola Review (Period 7)

Front

What is the vertex of a parabola?

Back

The highest or lowest point of a parabola.

Front

What does the value of 'a' in a quadratic equation indicate?

Back

The value of 'a' tells you the direction of the opening of the parabola.

Front

How can you determine if a parabola opens upwards or downwards?

Back

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

Front

What is the axis of symmetry in a parabola?

Back

The vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a) in the standard form y = ax^2 + bx + c.

Front

What is the standard form of a quadratic equation?

Back

y = ax^2 + bx + c, where a, b, and c are constants.

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, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you find the y-intercept of a parabola?

Back

Set x = 0 in the quadratic equation and solve for y.

Front

What is the formula for finding the vertex of a parabola in standard form?

Back

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

Front

What does it mean for a parabola to have a maximum or minimum value?

Back

A maximum value occurs at the vertex if the parabola opens downwards; a minimum value occurs if it opens upwards.

Front

How can you graph a parabola?

Back

Identify the vertex, axis of symmetry, y-intercept, and plot additional points to sketch the curve.