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Ierofanga [76]
2 years ago
14

Which of the following are the coordinates of the vertex of y = −x2 + 2x + 1? (2, 1) (1, –2) (1, 2) (–2, 1)

Mathematics
1 answer:
IceJOKER [234]2 years ago
3 0

Answer:

C

Step-by-step explanation:

We want to determine the vertex of the quadratic equation:

\displaystyle y = -x^2 + 2x + 1

Recall that the vertex is given by the formulas:

\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)

In this case, <em>a</em> = -1, <em>b</em> = 2, and <em>c</em> = 1.

Determine the <em>x-</em>coordinate of the vertex:

\displaystyle x = -\frac{(2)}{2(-1)} = 1

To determine the <em>y-</em>coordinate, evaluate the function at <em>x</em> = 1:

\displaystyle \begin{aligned} y(1)&= -(1)^2 + 2(1) + 1 \\ &= 2\end{aligned}

In conclusion, the vertex of the quadratic equation is (1, 2).

Hence, our answer is C.

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bulgar [2K]
I remember dis, yey

so if a polynomial has roots r_1, r_2, r_3, it can be factored into
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also, if a polynomial has rational coefients and a+bi is a root, then a-bi must also be a root


so our roots we need are
4,16, 1+9i and 1-9i

so assuming multiplity 1 (that means we have something like [/tex]f(x)=a(x-r_1)^1(x-r_2)^1(x-r_3)^1[/tex])

we get that your function is
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3 years ago
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Find a cubic function f(x) = ax^3 + bx^2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 a
Ahat [919]

Answer:

f(x) = (3x³ + 9x² - 27x + 15)/32

Step-by-step explanation:

f'(x) = 3ax² + 2bx + c

Maximum or minimum: f'(x) = 0

Maximum: f'(-3) = 0 and f(-3) = 3

Minimum: f'(1) = 0 and f(1) = 0

f'(-3) = 0 leads 27a - 6b + c = 0       (1)

f'(1) = 0 leads 3a + 2b + c = 0           (2)

f(-3) = 3 leads -27a + 9b -3c + d = 3    (3)

f(1) = 0 leads a + b + c + d = 0        (4)

(1) - (2):   24a - 8b = 0, or 3a - b = 0, b = 3a

(3) - (4)   -28a + 8b - 4c = 3    (5)

(1) * 4 + (5):  80a - 16b = 3,

use b = 3a, get 80a - 16*3a = 3, 32a = 3, a = 3/32, b = 3a = 9/32

From (2): c = -3a - 2b = -9/32 - 18/32 = -27/32

From (4): d = -a - b - c = -3/32 - 9/32 + 27/32 = 15/32

So

f(x) = (3x³ + 9x² - 27x + 15)/32

3 0
2 years ago
pls helpppp c=30m+50 and c=20m+100. solve for c and show your work.
Contact [7]

Answer:c=200

Step-by-step explanation:

30(5) + 50 = 200

20(5) + 100 = 200

-------------------------------|

100 30m

- 50 - 20m

——— ———

50 10m 50/10 = 5 [m=5]

7 0
3 years ago
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