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3 years ago

Subtract the polynomials.

Mathematics

2 answers:

Mama L [17]3 years ago

8 0

Answer:

Step-by-step explanation:

Given

(4x² - 3x - 4) - (3x² + 4x - 8) ← distribute by - 1

= 4x² - 3x - 4 - 3x² - 4x + 8 ← collect like terms

= x² - 7x + 4 → B

AleksAgata [21]3 years ago

8 0

Step-by-step explanation:

$(4 {x}^{2} - 3x - 4) - (3 {x}^{2} + 4x - 8) \\ \\ = 4 {x}^{2} - 3x - 4 - 3 {x}^{2} - 4x + 8 \\ \\ = 4 {x}^{2} - 3 {x}^{2} - 3x - 4x - 4 + 8 \\ \\ = {x}^{2} - 7x + 4$

Thus option B is the correct answer.

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GuDViN [60]

Answer:

vertex = (0, -4)

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Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

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Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

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