Use the one-proportion z-test to perform the specified hypothesis test. Use the critical-value approach.

What is the general form of the quadratic with vertex at (2, 3) and passing through the point (5, 12)?

ki77a [65]

The general form of the quadratic with vertex at (2, 3) and passing through the point (5, 12) is x²-4x+7.

<h3>What is the vertex form of a quadratic equation?</h3>

Vertex form of the quadratic equation is used to find the coordinate of vertex points at which it crosses its symmetry.

The standard equation of the vertex form of quadratic is given as,

$y=a(x-h)^2+k$

Here, (h, k) is the vertex point.

The vertex of quadratic at (2, 3) and passing through the point (5, 12). Put the value of vertex point in the above equation,

$y=a(x-2)^2+3$

As the quadratic passes through the point (5, 12). Thus, put the value of this point,

$12=a(5-2)^2+3\\12-3=a(3)^2\\9=a\times9\\a=\dfrac{9}{9}\\a=1$

Put the value of a in the above expression,

$y=1(x-2)^2+3\\y=(x-2)^2+3\\y=x^2-4x+4+3\\y=x^2-4x+7$

Thus, the general form of the quadratic with vertex at (2, 3) and passing through the point (5, 12) is x²-4x+7.

Learn more about the vertex form here;

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4 0

3 years ago

F(x) = -x^2+11x+18 G(x) = x+2 Find (f/g)(x)

iren2701 [21]

$\frac{f}{g} (x) = \frac{ {x}^{2} + 11x + 18 }{x + 2} \\ = \frac{(x + 2)(x + 9)}{x + 2} \\ = x + 9$

with x never -2

8 0

3 years ago

New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that o

frosja888 [35]

The answer is 80 square meters.

The square area is expressed as:
A = a²,
where A is the area of the square, and a is the side of the square.

The rectangle area is expressed as:
A₁ = a₁ · b₁,
where A₁ is the area of the rectangle, and a₁ and b₁ are the sides of the rectangle.

After renovations, square garden becomes rectangular.

One side is doubled in length:
a₁ = 2a

The other side is decreased by three meters.
b₁ = a - 3

The new area is 25% than the original square garden:
A₁ = A + 25%A =
= A + 25/100·A
= A + 1/25·A
= a² + 1/25·a²
= a² + 0.25·a²
 = 1.25·a²

If the starting equation is:
A₁ = a₁ · b₁

Thus, the equation is:
1.25a² = 2a·(a - 3)
1.25a² = 2a · a - 2a · 3
1.25a² = 2a² - 6a

Therefore, the equation that could be used to determine the length of a side of the original square garden is:
2a² - 6a = 1.25a²

Now, we will solve the equation:
2a² - 6a = 1.25a²
2a² - 1.25a² - 6a = 0
0.75a² - 6a = 0
⇒ a(0.75a - 6) = 0

From here, one of the multiplier must be zero - either a or (0.75a - 6). Since a could not be zero, (0.75a - 6) is:
0.75a - 6 = 0
0.75a = 6
a = 6 ÷ 0.75
a = 8

If the side of the square is 8, then the area of the rectangle is
A₁ = 1.25 · a²
A₁ = 1.25 ·8²
A₁ = 1.25 · 64
A₁ = 80

Therefore, the area of the new rectangle garden is 80 square meters.

4 0

4 years ago

Which sign makes this number sentence true?

Bumek [7]

Believe the answer is C

5 0

2 years ago

Quadrilateral ABCD has vertices A(1, 0) B(5, 0) C (7, 2) D(3, 2). Use slope to prove that ABCD is a parallelogram.

iogann1982 [59]

In here, we will use the slope formula in order to prove that ABCD is a parallelogram. The slope of AB must be equal to CD and the slope of BC must be equal to DA. Using the formula m = (y1-y2) / (x1-x2), we obtain the slope for AB = 0/4, BC = 1, CD = 0/4, DA = 1. We can say that ABCD is a parallelogram as it satisfies AB = CD, and BC = DA

6 0

3 years ago