Quadratic and Exponential Functions

What is a quadratic function?

• A polynomial function of degree 2, typically in the form of @@f(x) = ax^2 + bx + c@@, where a, b, and c are constants and a ≠ 0.

• A linear function represented by a straight line on a graph.

• A polynomial function of degree 3, typically in the form of @@f(x) = ax^3 + bx^2 + cx + d@@.

• A function that has a constant value, represented as @@f(x) = c@@.

How can you solve a quadratic equation by factoring?

• Express it in the form @@(px + q)(rx + s) = 0@@ and set each factor equal to zero to find the solutions.

• Use the quadratic formula @@x = rac{{-b ext{±} ext{√}(b^2 - 4ac)}}{{2a}}@@ to find the roots.

• Graph the equation and find the x-intercepts.

• Complete the square to rewrite the equation in vertex form.

What is the standard form of a quadratic equation?

• @@ax^2 + bx + c = 0@@

• @@x^2 + 2x + 1 = 0@@

• @@a(x - h)^2 + k = 0@@

• @@x^2 - 4 = 0@@

How do you determine the solutions of a quadratic equation graphically?

• By finding the y-intercepts of the parabola on the graph.

• By calculating the vertex of the parabola.

• By finding the x-intercepts of the parabola on the graph.

• By using the quadratic formula to solve for x.

What is an exponential function?

• An exponential function is a mathematical function of the form @@f(x) = ab^x@@, where a is a constant, b is the base (b > 0), and x is the exponent.

• An exponential function is a polynomial function of the form @@f(x) = ax^n@@, where a is a constant and n is a positive integer.

• An exponential function is a logarithmic function that grows at a constant rate.

• An exponential function is a trigonometric function that oscillates between -1 and 1.

What is the quadratic formula?

• @@x = rac{{-b \pm \\sqrt{{b^2 - 4ac}}}}{{2a}}@@

• @@x = rac{{-b}}{{2a}}@@

• @@x = -b \\pm \\sqrt{{b^2 + 4ac}}@@

• @@x = rac{{b \\pm \\sqrt{{b^2 - 4ac}}}}{{2a}}@@

What are the roots of a quadratic equation?

• The values of x that make the equation equal to zero, found using the quadratic formula.

• The coefficients of the equation that determine its shape.

• The maximum or minimum points of the parabola.

• The solutions to the equation when graphed on a number line.

What is the y-intercept of a quadratic function?

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

• The point where the graph intersects the y-axis, found by evaluating @@f(0) = c@@ in the standard form @@f(x) = ax^2 + bx + c@@.

• The maximum value of the function.

• The minimum value of the function.

What is the significance of the leading coefficient in a quadratic function?

• It determines the width of the parabola.

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

• It affects the vertex of the parabola.

• It indicates the number of x-intercepts.

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 the direction it opens.

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

• The midpoint of the parabola's width.