A function have just one output (y) for each input (x). A value of x cannot have different corresponding values of y.
Tables B, C and D have differnet values of y (outputs) to a value of x(input), those are not functions.
Table A has one output (y) for each input (x). As you can see the output (y) can be the same for two or more inputs (x). It is a function
T=0=>initial
s (0)=4.5=9/2
=>s(t)=-16t^2+64+9/2
use s(-b/2a) to find height
it will take -b/2a seconds to reach that height
n I tell a,b coefficients of some
Follow for Solutions.
Example:
This suggests two solutions,
and
.
However, upon plugging these solutions back into the equation, you get
which checks out, but
does not because
is defined only for
(assuming you're looking for real solutions only). So, we call
an extraneous solution, and the complete solution set (over the real numbers) is
.
Answer:
y = 2(x - 1)² + 1
Step-by-step explanation:
The equation of a quadratic function in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, 1), thus
y = a(x - 1)² + 1
To find a substitute (4, 19) into the equation
19 = a(4 - 1)² + 1
19 = 9a + 1 ( subtract 1 from both sides )
18 = 9a ( divide both sides by 9 ), thus
a = 2
y = 2(x - 1)² + 1 ← in vertex form
