Exam 3: Linear, Quadratic, Polynomial, and Rational Functions

Find a constant c such that the graph of y = x² + 8x + c has its vertex on the x-axis.

Find a number c such that the line containing the points (6,c) and (9, 6) has slope -2.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 64x² + 9y² = 36

Find a formula for the inverse function of the indicated function.

Expand the indicated expression.

Find a formula for the inverse function Of the indicated function.

Find the center and radius of the circle with equation (x - 16)² + (y + 18)² = 16.

Suppose that f is a function whose domain is the interval , with f(x) = x² + 2x + 17. What is the range of f ?

Find a number t such that the point lies on the line containing the points (1, 0) and (2, -2).

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 3x² - 2x + 10y² - 6y + 19 = -9

Find the function which is graphed below.

Find a constant c such that , where .

Find a formula for if and .

Factor x²⁴ - y¹² as nicely as possible.

Find the function which is graphed below.

Solve using the quadratic formula.

Find the distance between the points and . (Give the exact answer.)

Find the equation of the line in the xy-plane that contains the point (2, -2) and that is perpendicular to the line whose equation is . Write the equation in slope-intercept form.

Find a positive number w such that the points (5, -3), (w, 2), and (9, w) all lie on a straight line.

Find a formula for the inverse function of the indicated function.