Characteristics of Quadratic Functions Review

What is the significance of the y-intercept in a quadratic function?

• The y-intercept is the point where the graph intersects the y-axis, found by evaluating @@f(0)@@.

• The y-intercept represents the maximum value of the function.

• The y-intercept indicates the slope of the function at its vertex.

• The y-intercept is the point where the graph intersects the x-axis.

How do you determine the maximum or minimum value of a quadratic function?

• By finding the roots of the equation using the quadratic formula.

• By completing the square to rewrite the function in vertex form.

• The maximum or minimum value occurs at the vertex, which can be found using the formula @@k@@ from the vertex form @@f(x) = a(x - h)^2 + k@@.

• By evaluating the function at several points and identifying the highest or lowest value.

What is the vertex of a parabola?

• The point where the parabola intersects the x-axis.

• The highest or lowest point on the graph, depending on whether it opens upwards or downwards.

• The point where the parabola intersects the y-axis.

• The midpoint of the line segment connecting the focus and directrix.

What is the range of a quadratic function that opens downwards?

• (-∞, k] where k is the y-coordinate of the vertex

• [k, ∞) where k is the y-coordinate of the vertex

• (-∞, ∞)

• [k, 0) where k is the y-coordinate of the vertex

What is the discriminant of a quadratic equation?

• The discriminant is given by @@D = b^2 - 4ac@@ and determines the nature of the roots of the quadratic equation: if D > 0, two distinct real roots; if D = 0, one real root; if D < 0, no real roots.

• The discriminant is the sum of the coefficients of the quadratic equation.

• The discriminant is always a positive number.

• The discriminant indicates the maximum value of the quadratic function.

What is the effect of the coefficient 'a' on the graph of a quadratic function?

• It determines the direction of the parabola: if @@a > 0@@, it opens upwards; if @@a < 0@@, it opens downwards. It also affects the width of the parabola.

• It only affects the height of the vertex of the parabola.

• It has no effect on the graph of the quadratic function.

• It determines the color of the graph.

What is the interval of decrease for a quadratic function that opens downwards?

• (h, ∞)

• (-∞, h)

• (h, 0)

• (0, h)

What is the interval of decrease for a quadratic function that opens upwards?

• @@(- ext{∞}, h)@@, where @@h@@ is the x-coordinate of the vertex.

• @@(h, ext{∞})@@, where @@h@@ is the x-coordinate of the vertex.

• @@(- ext{∞}, 0)@@, where @@0@@ is the y-intercept.

• @@(0, ext{∞})@@, where @@0@@ is the y-intercept.

What does the axis of symmetry represent in a quadratic function?

• A vertical line that divides the parabola into two mirror-image halves, given by the equation @@x = h@@, where (h, k) is the vertex.

• A horizontal line that represents the maximum value of the quadratic function.

• A point that indicates the vertex of the parabola.

• A line that intersects the parabola at its roots.

What is the range of a quadratic function that opens upwards?

• @@[k, ext{∞})@@, where @@k@@ is the y-coordinate of the vertex.

• @@(- ext{∞}, k)@@, where @@k@@ is the y-coordinate of the vertex.

• @@(- ext{∞}, ext{∞})@@, since it can take any value.

• @@[k, ext{0})@@, where @@k@@ is the y-coordinate of the vertex.