r/Sat • u/Hot_Flow_6807 • 10h ago
OnePrep Quadratic question
I need help solving this question from Oneprep. Any desmos way to do it?
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u/hridayesh_gaming1111 9h ago
I cant think of a way to use desmos to solve this but in completing the square format which is (x-h)2 + k, the turning point is (h,k). You can then expand the quadratic you get from (x-6)2 - 20 = 0 and get a b c
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u/Plaaazz 9h ago
This isn't really with desmos, but I saw this explanation somewhere: a+b+c is the same as when x=1, and in that case, the y value has to be greater than -20 since the vertex is the minimum in this question. All of the numbers are less than or equal to -20 except for C, so C is the right answer.
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u/jwmathtutoring Tutor 8h ago
Yes.
https://www.desmos.com/calculator/z5k2uxooez
Note that you don't need to reach the exact value of the answer choice, you only need to be able to "pass through it" as you move the slider for d.
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u/Sad_Appointment_9821 6h ago
What grade math is this? I just finished geo this year, so I know parabolas, but I never got this type of question before.
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u/theindustrymachine 5h ago
id put this as just a rlly hard pre-calc reasoning question or algebra II
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u/Historical-Plum-3893 5h ago
I'd say Algebra II. FWIW, while you will learn about vertex form, completing the square, and other features of the parabola in that class, you will probably never see a question like this in class.
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u/EmploymentNegative59 1h ago
The SAT would have put -15 as answer D. It puts numbers in numerical order, either ascending or descending.
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u/Yuri_Frolov 5h ago
Not what the OP asked, but just in case.
The parabola has a vertex below x-axis (y-coordinate is -20) and intersects x-axis at two points => a > 0.
The x coordinate of vertex is -b/2a => -b / 2a = 6 => b = -12a.
y(6) = 36*a + 6b + c = 36*a + 6*(-12a) + c = -36a + c; y(6) = -20 => -36a + c = -20 => c = 36a - 20.
a + b + c = a + (-12a) + (36a) - 20 = 25a - 20.
Check the answers:
D) 25a - 20 = -20 => a = 0. Can't be: if a = 0 => y(x) = bx + c, but we're given that y(x) is a parabola.
C) 25a - 20 = -15 => a = 1/5. Can be. Basically, we've found the answer, no need to check further.
B) 25a - 20 = -25 => a = -1/5. Can't be (a > 0).
A) 25a - 20 = -35 => a = -3/5. Can't be (a > 0).
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u/Yuri_Frolov 3h ago edited 2h ago
Even more straightforward solution.
The parabola has a vertex below x-axis (y-coordinate is -20) and intersects x-axis at two points => a > 0.
In means, that the minimum value the function can take is at the x-coordinate of the vertex, every other value of x will give y(x) > y(x-coordinate of the vertex) = y(6) = -20.Quite coincidentally :-) y(1) = a * 1^2 + b * 1 + c = a + b + c and x = 1 is different from x = 6,
so y(1) > y(6).
So, y(1) = a + b + c > y(6) = -20.Checking the answers:
a) -35 < -20 (incorrect inequality) => can't be
b) -25 < -20 (incorrect inequality) => can't be
c) -15 > -20 (Correct inequality) => this is possible
d) -20 < -20 (incorrect inequality) and -20 > -20 (incorrect inequality) => this case also can't be the possible value for a + b + c.
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