Complete the square to rewrite the quadratic:
2 <em>x</em>² + 3 <em>x</em> + 5 = 2 (<em>x</em>² + 3/2 <em>x</em>) + 5
... = 2 (<em>x</em>² + 3/2 <em>x</em> + 9/16 - 9/16) + 5
... = 2 (<em>x</em>² + 3/2 <em>x</em> + (3/4)²) + 5 - 9/8
... = 2 (<em>x</em> + 3/4)² + 31/8
Any real number squared becomes non-negative, so the quadratic expression has a minimum value of 31/8, which is greater than 0, and so there are no (real) <em>x</em> for which <em>y</em> = 0.
-4/3 is C
-1/3 is B
-1.5 is A
Answer:
a.2s b.43.6m
Step-by-step explanation:
h(t)=−4.9t2+19.6t+24
24m = inittial possition
-4.9 t2= -1/2 g t2
19.6t= Vo t
as the initial velocity is positive, the ball is thrown up.
the maximum height of the ball is reached when the velocity is 0
V= Vo-gt=19.6m/s-9.8m/s2 t=0
t=19.6/9.8=2s
<u>it takes 2seconds for the ball to reach its maximum height</u>
h(t)=−4.9t2+19.6t+24
h(2)=-19.6m+39.2m+24=43.6m
<u>the maximum height of the ball is 43.6m</u>
Answer:
Step-by-step explanation:
