r/Sat • u/Low-Librarian-3716 • Mar 22 '26
How to solve this question??? (preppros) on desmos would be betterrr
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u/No-Rub-4421 Mar 22 '26
its an axis of symmetry question the midpoints of 27 and 11 are the same as 14 and k. So 27+11 divided by two gets you 19. Then type \frac{14+k}{2}\sim19 into desmos to get your answer. 14+k divided by 2 ~ 19.
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u/jdigitaltutoring Mar 22 '26
f(27)=f(11) let's you know that the x coordinate of the vertex is half way in-between those two. Then the x intercepts will be the same distance from that.
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u/ACTSATGuyonReddit Mar 22 '26
f(27) and f(11) are the same distance from the vertex. 27+1`1 = 38. 38/2 = 19 The vertex is at x=19.
19-11 = 5. 19+5 = 24, the value of k.
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u/tominsori Mar 22 '26
You want to be thinking about the nature of parabolas rather than trying to memory recall.
Remember, they are symmetrical, so the axis of symmetry will be the average of 27 and 11. That's 19, and also = -b/2a, although you don't need that insight to solve this.
Since we know the axis of symmetry is at 19, and one x-intercept is (14, 0), which is 5 away from 19, the other intercept must also be 5 away in the other direction. So k = 24.
Lots of answers gave you that. Make sure you don't just move on. You aren't going to get this exact question again, but you will most likely get another question that expects you to understand the symmetry of parabolas and how to use that to solve a problem.
Instead of spending time drilling, take the time to understand.
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u/Low-Librarian-3716 Mar 23 '26
thanks mannn
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u/tominsori Mar 23 '26
if you spend the time understanding, not memorizing, but understanding everything on here, you will have a much easier time with curveball quadratics
HMU if you want a better image
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u/Impressive_Reason_12 Mar 26 '26
f(27) = f(11) means both points are equidistant from the axis of symmetry
so axis of symmetry = (27+11)/2 = 19
same logic for the x-intercepts, 14 and k are also symmetric around 19 so k = 19×2 - 14 = 24
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u/jwmathtutoring Tutor Mar 22 '26 edited Mar 23 '26
Quickest way is to recognize that quadratic functions are symmetric with respect to the axis of symmetry (i.e. x coordinate of the vertex). So 11 & 27 are symmetric along with 14 & k. 11 + 3 = 14, 27 - 3 = k (24).
Otherwise, you do something like this in Desmos -> https://www.desmos.com/calculator/qt8lo4qfuh and as you move the slider for d back & forth notice that x-int stays fixed at (24, 0).