Parts of Parabola

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where the curve changes direction. It is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the vertex of the parabola given in standard form: y = ax^2 + bx + c?

Back

The vertex can be found using the formula: \( x = -\frac{b}{2a} \). Substitute this x-value back into the equation to find the y-coordinate.

Front

What is the axis of symmetry in 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: \( x = -\frac{b}{2a} \).

Front

Given the equation y = (x + 10)(x + 6), find the vertex.

Back

The vertex is (-8, -8).

Front

Given the equation y = x^2 + 6x + 2, find the vertex.

Back

The vertex is (-3, -7).

Front

If the axis of symmetry is x = 4, what is the vertex of the parabola described by y = -2x^2 + 16x - 12?

Back

The vertex is (4, 20).

Front

What is the standard form of a parabola?

Back

The standard form of a parabola is given by: \( y = a(x - h)^2 + k \), where (h, k) is the vertex.

Front

What does the 'a' value in the standard form of a parabola indicate?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

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

Back

If the coefficient 'a' in the equation y = ax^2 + bx + c is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

Front

What is the significance of the vertex in real-world applications?

Back

The vertex can represent maximum or minimum values in real-world scenarios, such as profit maximization or cost minimization.