All categories

3 years ago

Can you help me im not that good at math and its a clear photo y =_x^2+x+______

Mathematics

1 answer:

geniusboy [140]3 years ago

3 0

Vertex/General Form: y = a(x - h)^2 + k, with (h,k) as the vertex
(x + y)^2 = x^2 + 2xy + y^2
Standard Form: y = ax^2 + bx + c

So before I put the equation into standard form, I'm first going to be putting it into vertex form. Since the vertex appears to be (-1,7), plug that into the vertex form formula:

$y=a(x-(-1))^2+7\\y=a(x+1)^2+7$

Next, we need to solve for a. Looking at this graph, another point that is in this line is the y-intercept (0,5). Plug (0,5) into the x and y placeholders and solve for a as such:

$5=a(0+1)^2+7\\5=a(1)^2+7\\5=a+7\\-2=a$

Now we know that our vertex form equation is y = -2(x + 1)^2 + 7.

However, we need to convert this into standard form still, and we can do it as such:

Firstly, solve the exponent: $y = -2(x^2+2x+1) + 7$

Next, foil -2(x^2+2x+1): $y = -2x^2-4x-2+7$

Next, combine like terms and your final answer will be: $y = -2x^2-4x+5$ 

You might be interested in

A triangle has a perimeter of 126 centimeters. The 2 longer sides are 3 times as long as the shortest side. Find the length of e

Vladimir [108]

The shorter side of the triangle is 18 cm and each of the longer sides are 54 cm

Solution:

Given that triangle has perimeter of 126 cm

Let the length of the shorter side of the triangle be "a"

The 2 longer sides are 3 times as long as the shortest side

So length of 2 longer sides = 3(length of the shorter side)

length of 2 longer sides = 3a

The perimeter of triangle is given as:

perimeter of triangle = length of the shorter side + length of 2 longer sides

perimeter of triangle = a + 3a + 3a

126 = a + 3a + 3a

7a = 126

a = 18

So length of shorter side = 18 cm

length of 2 longer sides are each = 3a = 3(18) = 54 cm

Thus, the shorter side of the triangle is 18 cm and each of the longer sides is 54 cm

4 0

3 years ago

What percent of 43.75 is 70

Pavlova-9 [17]

1.6 % of 43.75 is 70
Because 70/43.75 is 1.6

4 0

3 years ago

1. Derive the half-angle formulas from the double

lilavasa [31]

1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

<h3>How to apply trigonometry on deriving formulas and transforming points</h3>

1) The following trigonometric formulae are used to derive the half-angle formulas:

sin² θ / 2 + cos² θ / 2 = 1 (1)

cos θ = cos² (θ / 2) - sin² (θ / 2) (2)

First, we derive the formula for the sine of a half angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a half angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a half angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in rectangular form to polar form are obtained by trigonometric functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in polar form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in rectangular form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the linear function y = 5 · x - 8, we proceed to use the following substitution formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

To learn more on trigonometric expressions: brainly.com/question/14746686

#SPJ1

4 0

2 years ago

I need help with this ASAP!!

liraira [26]

Answer:=

−243 /512 Fraction

4 0

3 years ago

In the Minnesota Northstar Cash Drawing, you pick five different numbers between 1 and 35. What is the probability of picking th

maw [93]

Answer:

$\frac{1}{324632}$ probability of picking the winning combination

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Since the order is not important, the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

The correct five numbers from a set of 5. So

$D = C_{5,5} = \frac{5!}{5!0!} = 1$

Total outcomes:

Five numbers from a set of 35. So

$T = C_{35,5} = \frac{35!}{5!30!} = 324632$

Probability:

$p = \frac{D}{T} = \frac{1}{324632}$

$\frac{1}{324632}$ probability of picking the winning combination

5 0

2 years ago

Can you help me im not that good at math and its a clear photo y =___x^2+__x+______

Can you help me im not that good at math and its a clear photo y =_x^2+x+______