COLLEGE BOARD Test 9 Math Section 3 #13

COLLEGE BOARD Test 9 Math Section 3 #13

Could you suggest a shortcut or fast way to solve this? All the answers are written in vertex form, so we can quickly eliminate two of them, as the coordinates of the vertex, as indicated by the graph provided, must be (3,1). That leaves choices A and C. Is there a quick way to solve from there without plugging in values from the graph?

PWN the SAT Parabolas drill explanation p. 325 #10

PWN the SAT Parabolas drill explanation p. 325 #10: The final way to solve: If we are seeking x=y, since the point is (a,a), why can you set f(x) = 0? You start out with the original equation in vertex form, making y=a and x=a, but halfway through you change to y=0 (while x is still = a). How can we be solving the equation when we no longer have a for both x and y?

A tennis ball is thrown upward from the ground and its height, h, is given by the equation h=22t – t^2. Some kids are sitting on the roof of a building that stands 21 feet tall. If the kids are sitting in such a position that they cannot see the ball until it reaches the height of the roof, for how many seconds of the tennis ball’s flight can the kids see the ball? A- 18 B-20 C-21 D-22

Basically, the question is: how many seconds is h greater than 21? (This tennis ball is being thrown on a planet other than Earth, by the way. I challenge anyone to throw a tennis ball that stays in the air anywhere near as long as this one does.) To figure it out, solve for the (more…)

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

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

PWN p. 157 #8

In PWN p. 159 (p. 157 later printing) #8
In the xy-plane, where a and b are constants, the graphs …

The question does not specify that a and b are positive values. If one or both were negative, wouldn’t that change the answer?

Question number 6 from the Parabola chapter

Hi, Mike! Can you explain the second way we can approach question number 6 from the Parabola chapter? (The two points where the higher y-coordinate is also farther from the line of symmetry.) It would be great if you can provide an example. Thank you.