Parts 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 parabola in the form y = ax^2 + bx + c.

Front

What does it mean if a parabola has a minimum?

Back

A parabola has a minimum when it opens upwards, meaning the vertex is the lowest point on the graph.

Tags

CCSS.HSF-IF.C.7A

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

How do you find the zeros of a parabola?

Back

The zeros (or x-intercepts) of a parabola can be found by solving the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Tags

CCSS.HSF-IF.C.7A

Front

What is the standard form of a parabola's equation?

Back

The standard form of a parabola's equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in the parabola's equation indicate?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What is the significance of the 'b' value in the parabola's equation?

Back

The 'b' value affects the position of the vertex along the x-axis and the axis of symmetry.

Tags

CCSS.HSF-IF.C.7A

Front

What is the significance of the 'c' value in the parabola's equation?

Back

The 'c' value represents the y-intercept of the parabola, which is the point where the graph crosses the y-axis.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

If the 'a' value 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 formula to find the vertex of a parabola in standard form?

Back

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