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 by the equation 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^2 + 6x + 2, find the vertex.

Back

The vertex is (-3, -7).

Front

Identify the vertex of the parabola represented by the equation y = (x + 10)(x + 6).

Back

The vertex is (-8, -8).

Front

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

Back

The vertex is (4, 20).

Front

What does the term 'parabola' refer to in mathematics?

Back

A parabola is a symmetric curve formed by the intersection of a cone with a plane parallel to its side. It can open upwards or downwards.

Tags

CCSS.7.G.A.3

Front

What is the standard form of a parabola?

Back

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

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.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

The 'a' value determines 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.