What is the best way to solve this problem within ~1 minute? (given SAT time limit)

Hi Mike …can you solve & explain? (from QAS March 2021)

Section 3; #11.

y = (x-1)(x+1)(x+2)

The graph in the xy plane of the equation above contains the point (a,b). If -1 < or = a < or = 1, which of the following is NOT a possible value of b?

A) -2

B) -1

C) 0

D) 1

f(x) = √x

g(x) = 3x – b

If the graph of y = f(g(x)) passes through (6, 5) in the standard (x, y) coordinate plane, what is the value of b?

The midpoint formula tells you that the a segment with endpoints (a, b) and (c, d) will have a midpoint at ((a + c)/2,(b + d)/2) So we know that (x + 9)/2 = 6 and (5 + y)/2 = 3. We can solve those! (x + 9)/2 = 6 x + 9 = 12 x = 3 (5 + y)/2 = 3 5 + y = (more…)

Draw this out. Start with the two points you’re given. Now remember that the shape is a rectangle, and that you’re told that point B is on the x-axis. The only way that happens is if B is at (5, 0). Point D, by the same logic, must be at (–3, 2). Now draw the rectangle (more…)

The thing to remember about functions is that they do the same thing to whatever is inside the parentheses. So don’t worry about the r vs. the h. They could use x, or a little star symbol, or whatever else they want. What matters is that the function f, as defined here, will equal zero (more…)

A question from the May 2018 SAT (Section 4 #18)

kx + y = 1

y = -x² + k

In the system of equations above, k is a constant. When the equations are graphed in the xy-plane, the graphs intersect at exactly two points. Which of the following CANNOT be the value of k?

A. 3

B. 2

C. 1

D. 0

Here are a couple questions from the old official SAT Subject Test Math I practice exam:

The function f is defined by f(x) is x^4 – 4x^2 + x + 1 for -5 ≤ x ≤ 5. In which of the following intervals does the minimum value of f occur?

A) -5 ≤ x ≤ -3

B) -3 ≤ x ≤ -1

C) -1 ≤ x ≤ 1

D) 1 ≤ x ≤ 3

E) 3 ≤ x ≤ 5

Can you solve w/o graphing?

Could you please explain SAT Past paper 3, section 4, question 12? I don’t really understand why the double root is considered a ‘distinct’ zero.

Thank you for your time!

Can you help me with the Official Test 4 Question 21?

Test 8 Section 4 #30

what is the difference between the maximum value of y=-x^4-2x^3+5 and the minimum value of y = x^4+x^2-4

PSAT #2, Section 4, #29

Test 5, Section 4, Question 20. How do you get to the answer?

If r>0 and (9r/2)^(1/3) = (1/2) r, what is the value of r?