Math 110 Exam 2 Calculus, Polynomial, and
Exponential Applications Complete Review
(2026) | 100% Verified Responses | A+
• Difference Quotient -✓✓[f(a+h) - f(a)]/h — used to find the slope of a
secant line.
• Domain of a function -✓✓All real numbers except where undefined.
• Finding the domain -✓✓1II Identify all x-values that make the
function undefined. 2II Denominators ≠ 0; even roots must have
nonnegative radicands; logs require positive arguments.
• Quadratic in vertex form -✓✓Complete the square: For f(x) = ax² + bx
+ c, factor a (if ≠1), then rewrite as a(x - h)² + k, where h = -b/(2a) and k
= f(h). Vertex = (h, k).
• Max/Min of a quadratic function -✓✓If a > 0, parabola opens up ⇒
vertex is minimum. If a < 0, parabola opens down ⇒ vertex is
maximum. Use vertex formula (h = -b/2a, k = f(h)).
• Sketching a quadratic function -✓✓1II Find vertex (h,k) 2II Find y-
intercept (x=0) 3II Find x-intercepts (solve ax²+bx+c=0) 4II Plot
symmetry about x=h 5II Sketch curve opening up/down depending on
sign of a.
, • Max height of a ball's path -✓✓Use vertex formula: h = -b/(2a) = -
64/(2×-16)=2. Then y(2) = -16(4)+64(2)+5=69. Max height = 69 ft.
• Horizontal distance traveled by the ball -✓✓Set y=0 and solve -
16x²+64x+5=0. Use quadratic formula: x = [-64 ± √(64²-4(-16)(5))]/(2(-
16)). Only positive root = horizontal distance traveled.
• Sketching a polynomial function -✓✓1II Find all zeros (x-intercepts)
and multiplicities. 2II Determine end behavior from leading term. 3II
Determine y-intercept (x=0). 4II Sketch with correct turning points and
crossing/bouncing behavior.
• Dividing polynomials -✓✓Use long or synthetic division. Divide the
highest-degree terms, multiply back, subtract, repeat. Result: quotient +
remainder/divisor.
• Rational Zero Theorem -✓✓Possible rational zeros = ±(factors of
constant term)/(factors of leading coefficient). Test each using synthetic
division.
• Descartes' Rule of Signs -✓✓Count sign changes in f(x) ⇒ # of
positive real roots or fewer by even numbers. Count sign changes in f(-
x) ⇒ # of negative real roots.
Exponential Applications Complete Review
(2026) | 100% Verified Responses | A+
• Difference Quotient -✓✓[f(a+h) - f(a)]/h — used to find the slope of a
secant line.
• Domain of a function -✓✓All real numbers except where undefined.
• Finding the domain -✓✓1II Identify all x-values that make the
function undefined. 2II Denominators ≠ 0; even roots must have
nonnegative radicands; logs require positive arguments.
• Quadratic in vertex form -✓✓Complete the square: For f(x) = ax² + bx
+ c, factor a (if ≠1), then rewrite as a(x - h)² + k, where h = -b/(2a) and k
= f(h). Vertex = (h, k).
• Max/Min of a quadratic function -✓✓If a > 0, parabola opens up ⇒
vertex is minimum. If a < 0, parabola opens down ⇒ vertex is
maximum. Use vertex formula (h = -b/2a, k = f(h)).
• Sketching a quadratic function -✓✓1II Find vertex (h,k) 2II Find y-
intercept (x=0) 3II Find x-intercepts (solve ax²+bx+c=0) 4II Plot
symmetry about x=h 5II Sketch curve opening up/down depending on
sign of a.
, • Max height of a ball's path -✓✓Use vertex formula: h = -b/(2a) = -
64/(2×-16)=2. Then y(2) = -16(4)+64(2)+5=69. Max height = 69 ft.
• Horizontal distance traveled by the ball -✓✓Set y=0 and solve -
16x²+64x+5=0. Use quadratic formula: x = [-64 ± √(64²-4(-16)(5))]/(2(-
16)). Only positive root = horizontal distance traveled.
• Sketching a polynomial function -✓✓1II Find all zeros (x-intercepts)
and multiplicities. 2II Determine end behavior from leading term. 3II
Determine y-intercept (x=0). 4II Sketch with correct turning points and
crossing/bouncing behavior.
• Dividing polynomials -✓✓Use long or synthetic division. Divide the
highest-degree terms, multiply back, subtract, repeat. Result: quotient +
remainder/divisor.
• Rational Zero Theorem -✓✓Possible rational zeros = ±(factors of
constant term)/(factors of leading coefficient). Test each using synthetic
division.
• Descartes' Rule of Signs -✓✓Count sign changes in f(x) ⇒ # of
positive real roots or fewer by even numbers. Count sign changes in f(-
x) ⇒ # of negative real roots.
