Function f is represented by the equation given below. Function g has a vertex at (2,4) and the parabola opens downwards. Which
of the following statements is true? The y-intercept of function f is less than the y-intercept of function g. The minimum of function f is at (-5,6). The y-intercept of function f is greater than the y-intercept of function g. The minimum of function g is at (2,4).
1 answer:
The complete question in the attached figure
we have that
f(x)=x²-5x+6
and <span>g(x) has a vertex at (2,4) and the parabola opens downwards
using a graph tool
see the attached figure
</span><span> statements
a) </span><span>The y-intercept of function f is less than the y-intercept of function g
this is not correct, because the </span>y-intercept of function f is greater than the y-intercept of function g
b) <span>The minimum of function f is at (-5,6)
this is not correct, because the minimum of function f is at (2.5,-0.25)
c)</span><span>The y-intercept of function f is greater than the y-intercept of function g
this is correct
d) </span><span>The minimum of function g is at (2,4)
this is not correct because the maximum of function g is </span>(2,4)
the answer is the option
The y-intercept of function f is greater than the y-intercept of function g
we have that
f(x)=x²-5x+6
and <span>g(x) has a vertex at (2,4) and the parabola opens downwards
using a graph tool
see the attached figure
</span><span> statements
a) </span><span>The y-intercept of function f is less than the y-intercept of function g
this is not correct, because the </span>y-intercept of function f is greater than the y-intercept of function g
b) <span>The minimum of function f is at (-5,6)
this is not correct, because the minimum of function f is at (2.5,-0.25)
c)</span><span>The y-intercept of function f is greater than the y-intercept of function g
this is correct
d) </span><span>The minimum of function g is at (2,4)
this is not correct because the maximum of function g is </span>(2,4)
the answer is the option
The y-intercept of function f is greater than the y-intercept of function g
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Answer:
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Step-by-step explanation:
Given that M is a polynomial of degree 3.
So, it has three zeros.
Let the polynomial be
M(x) =a(x-p)(x-q)(x-r)
The two zeros of the polynomial are -4 and 4i.
Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.
Then,
M(x)= a{x-(-4)}(x-4i){x-(-4i)}
=a(x+4)(x-4i)(x+4i)
=a(x+4){x²-(4i)²} [ applying the formula (a+b)(a-b)=a²-b²]
=a(x+4)(x²-16i²)
=a(x+4)(x²+16) [∵i² = -1]
=a(x³+4x²+16x+64)
Again given that M(0)= 53.12 . Putting x=0 in the polynomial
53.12 =a(0+4.0+16.0+64)
=0.83
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
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Answer:
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Step-by-step explanation:
Look at the photo below for the details.
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