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3 years ago

The vertex of the parabola below is at the point (4, -1). Which of the equations below could be the one for this parabola?

1 answer:

6 0

One possible equation for this quadratic would be

y=(x-4)²-1. This is vertex form: y=a(x-h)²+k, where (h, k) is the vertex.

However, this is not the only possible equation. There could be multiple values for a, in front of the parentheses, that we don't know about from the information we are given.

We can also write this equation in standard form (y=ax²+bx+c). First write the squared binomial as the product of two binomials:
y=(x-4)(x-4)-1

Multiply the binomials:
y=x*x-4*x-4*x-4(-4)-1
= x²-4x-4x--16-1
= x²-8x+16-1
= x²-8x+15

Again, this would change depending on what the value of a is in the functoin.

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Find the surface area of the right triangular prism shown

Inessa05 [86]

The surface area of the triangular prism is 144 cm²

Explanation:

Given:

Base of the triangle = 4

Height of the triangle = 3

Hypotenuse of the triangle = 5

Length of the prism = 11

Surface area of the rectangular prism = ?

Surface area, A = $ah+bh+ch+\frac{1}{2} \sqrt{-a^4 + 2(ab)^2 + 2(ac)^2 - b^4 + 2(bc)^2 - c^4}$

On substituting the value, we get:

$A = 4 X 11+ 3X11+5X11+\frac{1}{2} \sqrt{-(4)^2 + 2(4X3)^2 + 2(4X5)^2 - 3^4 + 2(3X5)^2-5^4} \\\\A = 144 cm^2$

Therefore, the surface area of the triangular prism is 144 cm²

6 0

2 years ago

Solve for w. -3(-8w+1) -w=5(w-1)-1 Simplify your answer as much as possible. W =

oksian1 [2.3K]

Answer:

W = - 6

Step-by-step explanation:

-3(-8w+1) - w = 5(w-1) - 1 -> (Original equation)

24w - 3 - w = 5w - 5 - 1 -> (Expanded version)

23w - 3 = 5w - 6 -> (Simplified version)

18w - 3 = - 6 -> (Subtract 5w from both sides)

18w = - 3 -> (Add 3 to both sides)

w = 18/-3 which is - 6 -> (Doing 18/-3)

5 0

2 years ago

Which statement is true

igomit [66]

it is c. because the function is not a dependent or independent variable

8 0

2 years ago

What are the endpoint coordinates for the midsegment of △BCD that is parallel to BC?

natulia [17]

Answer:

The endpoint coordinates for the mid-segment are: $(-2,-1)$ and $(1,0)$

Step-by-step explanation:

According to the given diagram, the coordinates of the vertices of $\triangle BCD$ are: $B(-3,1), C(3,3)$ and $D(-1,-3)$

Now, the endpoints of the mid-segment of $\triangle BCD$ which is parallel to $BC$ will be the mid-points of sides $BD$ and $CD$ .

Formula for the coordinate of mid-point : $(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})$ , where $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are two endpoints.