Can you explain this Q #29 from Calculator section of Oct 2022 PSAT:
A quadratic function can be used to model the height, in feet, of an object above the ground in terms of time, in seconds, after the object was launched. According to the model, an object was launched into the air from a height of 0 feet and reached its maximum height of 3136 feet 14 seconds after it was launched. Based on the model, what was the height, in feet, of the object 1 second after it was launched?
HI Mike…Thanks for all your help ! Here’s another question:
When a buffet restaurant charges $12.00 per meal, the number of meals it sells per day is 400. For each $0.50 increase to the price per meal, the number of meals sold per day decreases by 10. What is the price per meal that results in the greatest sales, in dollars, from meals each day?
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?
I do not understand question #4 pg 156 advanced systems of equations?
y=c(x^2) + d
In the systems of equations above, c and d are constants . For which of the following values of c and does the system of equations have no real solutions?
A) c=-6, d=6
B) c=-5, d=4
C) c=6, d=4
D) c=6, d=5
Please help, thank you.
Test 10 section 4 number 28
Is there a way to solve this system of equations without using the quadratic formula (or graphing)?
f(x) = –2/3 x + 4
g(x) = 3(x + 2)^2 – 4
How many solutions does the system above have?
Huge shortcut here if you just know that for a parabola in standard ax^2 + bx + c form, the x-coordinate of the vertex will be at –b/(2a). In this case, that means it’s at –3/(2(–6)) = 3/12 = ¼. from Tumblr https://ift.tt/2CRW93a
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?
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)
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?
Hi Mike, Can you please explain Question 11, Test 6, section 3 ? I know the parabola opens downward, but I’m confused after that. Thanks.
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?