Characteristics of Parabolas

Front

What is the axis of symmetry of a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic in standard form y = ax² + bx + c.

Front

What is the standard form of a quadratic equation?

Back

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

Front

Describe the end behavior of a parabola that opens upwards.

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

What is the vertex of a parabola?

Back

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

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum vertex, and the y-values increase as x moves away from the vertex.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum vertex, and the y-values decrease as x moves away from the vertex.

Front

How can you determine if a parabola has a maximum or minimum?

Back

You can determine this by looking at the coefficient 'a' in the standard form y = ax² + bx + c. If 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward or downward) and affects the width of the parabola. A larger absolute value of 'a' makes the parabola narrower.

Front

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

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(h) is the value of the quadratic function at x = h.

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis, found by evaluating the quadratic equation at x = 0, which gives y = c.