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3 years ago

13

Write the quadratic equation y=x^2-6x+7 in vertex form

1 answer:

Mazyrski [523]3 years ago

4 0

Using the formula x = b/(-2a) to find the x of the vertex you can find y of the vertex and plug into y = a(x - h)² + k where (h, k) is the vertex

h = x = -6/(-2×1) = 3
k = y = (3)² - 6(3) + 7 = -2
a = 1 because it is the coefficient of x² in y = ax² + bx + c

Answer: y = (x - 3)² - 2

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$\huge \bf༆ Answer ༄$

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ANTONII [103]

Answer:

(a) $s(44) = 3.52*10^{6}ft$

(b) $v(44) = 10*x^{5} ft/s$

(c) $a(44) = 3636ft/s^{2}$

Step-by-step explanation:

$s(t) = 1818t^{2}$

(a) when t = 44sec

$s(44) = 1818(44^{2}) = 1818(1936)\\ \\s(44) = 3519648ft$

s(44) ≅ $3520000=3.52*10^{6}ft$

(b) How fast the hammer is traveling i.e. the speed of the hammer.

To find speed, we differentiate the distance s(t) with respect to time, t

$speed,v=\frac{ds(t)}{dt}=\frac{d}{dt}(1818t^{2}) \\\\v = 1818*2t^{2-1}= 1818*2t\\ \\v = 3636t$

at t = 44sec,

$v = 3636*44=159984ft/s$

$v$ ≅ $160000ft/s = 1.6*10^{5}ft/s$

(c) The hammer's acceleration can be obtained by differentiating the speed v(t) with respect to time, t

$acceleration, a = \frac{dv}{dt}=\frac{d}{dt}(3636t)\\ \\a = 3636*1= 3636\\\\a = 3636ft/s^{2}$

There's no need to substitute t = 44sec because the acceleration is independent of time.

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