Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.
1 answer:
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Answer:
8x² +36x -27=0
Step-by-step explanation:
2x²= 6x +3
Let's rewrite the equation into the form of ax²+bx+c= 0.
2x² -6x -3=0
Thus, a= 2
b= -6
c= -3
Sum of roots=
Since your roots are p and q, sum of roots= p +q
p +q=
p +q= 6 ÷2
p +q= 3
Product of roots=
pq=
<u>Quadratic equations</u><u>:</u>
x² -(sum of roots)x +(product of roots)= 0
Thus, we have to find the sum and the product of the new roots, p²q and pq².
p +q= 3
pq= -3/2
Product of new roots
= (p²q)(pq²)
= p³q³
= (pq)³
sum of new roots
= p²q +pq²
= pq(p +q)
= (-3/2)(3)
= -9/2
Thus, the quadratic equation with roots p²q and pq² is
x² -(-9/2)x -27/8 = 0
Multiply by 8 throughout:
Answer:
see below
Step-by-step explanation:
C. The zeros can be read from the x-intercepts of the graph.
The zeros are -20, -5, +15.
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D. For zero "p", a linear factor will be (x -p). The linear factors are ...
(x +20), (x +5), (x -15)
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B. The factored form of the function is ...
f(x) = a(x +20)(x +5)(x -15) . . . . . for some scale factor "a"
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E. The standard form of the function will be the multiplied-out version of the factored form:
f(x) = a(x^3 +10x^2 -275x -1500)
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A. Using the distributive property, the full expanded standard form is ...
f(x) = ax^3 +10ax^2 -275ax -1500a
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F. The graph shows the y-intercept to be y=1. The function of parts E and/or A show the constant to be -1500a, so we have ...
-1500a = 1
a = -1/1500
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G. The graphed function is ...
f(x) = (-1/1500)(x^3 +10x^2 -275x -1500)
See the attachment for a graph.
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<em>Disclaimer</em>
We have tried to decipher the question's parts and to put them in an order corresponding to the way the problem is actually solved. It isn't clear exactly how "multiplied-out" the function is supposed to be at any stage. We have chosen to avoid having fractional coefficients, which may not be what you are expected to do.
