Parabola Review

Front

What is a parabola?

Back

The graph of a quadratic function, which is U-shaped and can open either upward or downward.

Front

What determines the direction a parabola opens?

Back

The value of 'a' in the quadratic equation y = ax^2 + bx + c. If 'a' is positive, it opens upward; if 'a' is negative, it opens downward.

Front

What is the vertex of a parabola?

Back

The highest or lowest point of the parabola, depending on its direction. It represents the maximum or minimum value of the quadratic function.

Front

How can you find the vertex of a parabola given the equation y = ax^2 + bx + c?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a). Substitute this value back into the equation to find the y-coordinate.

Front

What is the axis of symmetry in a parabola?

Back

A vertical line that divides the parabola into two mirror-image halves, which passes through the vertex. Its equation is x = -b/(2a).

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 'a' value in the quadratic equation?

Back

It affects the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.

Front

What is the formula for the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of the quadratic equation.

Front

What does the discriminant (b² - 4ac) tell us about a parabola?

Back

It indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root (the vertex); if negative, there are no real roots.

Front

If a parabola opens downward, what can we say about its vertex?

Back

The vertex is the maximum point of the parabola.