Graphing parabolas

Front

What is a parabola?

Back

A parabola is a symmetric curve formed by the graph of a quadratic function, represented by the equation y = ax^2 + bx + c.

Front

What does the coefficient 'a' in the equation of a parabola indicate?

Back

The coefficient 'a' determines the direction of the parabola's opening: if 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

How do you find the y-intercept of a parabola?

Back

To find the y-intercept, set x = 0 in the equation of the parabola and solve for y.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula V(-b/2a, f(-b/2a) for the quadratic equation y = ax^2 + bx + c.

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 = -b/2a.

Front

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

Back

If 'a' is positive, the parabola has a minimum value at the vertex. If 'a' is negative, it has a maximum value at the vertex.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you convert the standard form of a quadratic equation to vertex form?

Back

To convert to vertex form, complete the square: y = a(x-h)^2 + k, where (h, k) is the vertex.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you graph a parabola?

Back

To graph a parabola, find the vertex, axis of symmetry, y-intercept, and additional points, then plot and connect them smoothly.