A school allots £3000 to spend on a trip to the theatre.

Write 1/3 x^2 - 4x + 17 in vertex form

Svetradugi [14.3K]

Answer:

f(x)=−4(x+ 41 ) 2 − 4 11

Explanation:

The given function is

f(x) = - 4 {x}^{2} - 2x - 3f(x)=−4x 2 −2x−3

To write the function is vertex form, we need to complete the square.

We first factor -4 to get:

f(x) = - 4 ({x}^{2} + \frac{1}{2} x) - 3f(x−4(x2 + 21 x)−3

Add and subtract the square of half the coefficient of x.

f(x) = - 4( {x}^{2} + \frac{1}{2} x + \frac{1}{16} ) - \frac{1}{4} - 3f(x)=−4(x 2 + 21 x+ 16 1 )− 41 −3

We factor the perfect square trinomial and simplify to get:

f(x) = - 4( {x + \frac{1}{4} )}^{2} - \frac{11}{4}f(x)=−4(x+ 41 ) 2 − 4 11

8 0

3 years ago

Solve the equation uding the most direct method: 3x(x+6)=-10?

Tanzania [10]

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

<h3>Distribute</h3>

Use the distributive property to distribute 3x into the term (x + 6):

$3x(x+6)=-10$

$3x^2+18x=-10$

<h3>Rearrange</h3>

To create a quadratic equation, add 10 to both sides of the equation:

$3x^2+18x+10=-10+10$

$3x^2+18x+10=0$

<h3>Use the Quadratic Formula</h3>

The quadratic formula is defined as:

$\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

a = 3
b = 18
c = 10

Set up the quadratic formula:

$\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}$

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

$\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}$

Simplify the radicand:

$\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}$

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

$\sqrt{4\times51}$

Then, using the Product Property of Square Roots, break this into two radicands:

$\sqrt{4} \times \sqrt{51}$

Since 4 is a perfect square, it can be evaluated:

$2 \times \sqrt{51}$

To simplify further for easier reading, remove the multiplication symbol:

$2\sqrt{51}$

Then, substitute for the quadratic formula:

$\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}$

This gives us a combined root, which we should separate to make things easier on ourselves.

<h3>Separate the Roots</h3>

Separate the roots at the plus-minus symbol:

$\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}$

$\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}$

Then, simplify the numerator of the roots by factoring 2 out:

$\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}$

$\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}$

Then, simplify the fraction by reducing 2/6 to 1/3:

$\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}$

$\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}$

The final answer to this problem is:

$\displaystyle x=\frac{-9 + \sqrt{51}}{3}$

$\displaystyle x=\frac{-9 - \sqrt{51}}{3}$

3 0

2 years ago

Jessica has $24 and plans to spend it all at the grocery store. She wants to purchase bags of carrots and bagels. Bags of carrot

Andrei [34K]

2x+3y=24 is the equation-------------------------

6 0

4 years ago

Read 2 more answers

A, B, C, OR D ?!?!??!?!?!?!?

nadezda [96]

The answer would be letter A

7 0

3 years ago

Find the missing angle.

Tems11 [23]

Check the picture below.

make sure your calculator is in Degree mode.

but will run you about 36.8698976458° and 53.13010235415598°.

8 0

3 years ago