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Serga [27]
3 years ago
12

When written in standard form, the leading coefficient of the equation of a parabola that opens up will be- a fraction zero a wh

ole number negative an integer positive
Mathematics
1 answer:
kirill115 [55]3 years ago
8 0

Answer:

Positive integer

Step-by-step explanation:

A parabola is the locus of a point which is equidistant from a fixed point and a fixed line. The fixed line is known as the directrix, while the fixed point is known as the focus.

The axis of a parabola passes through the focus and is perpendicular to the directrix. The axis touches the parabola at a point known as the vertex.

The standard form of a parabola that opens up is:

4ay = x²;

where the focus is at (0, a), the equation of the axis is x = 0 and the equation of the directrix is y = -a (parallel to the y axis).

Hence, the leading coefficient of the equation of a parabola that opens up will be a positive integer.

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1 8/21 liters

Step-by-step explanation:

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3 years ago
look at this equation and the steps used to solve it. Which answer is the best justification for step 1 of this solution
Julli [10]

Answer:

Step-by-step explanation:

4 0
3 years ago
Please help!!! i'll give brainliest and offering 20 pts each!!!
Aleks04 [339]

Answer:

  • 5(x +1.5)^2
  • 10(x +1)^2
  • 1/4(x +2)^2
  • 3(x +5/6)^2

Step-by-step explanation:

When your desired form is expanded, it becomes ...

  a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2

This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.

a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2

b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2

c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2

d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2

_____

<em>Additional comment</em>

If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.

8 0
2 years ago
Find the slope of the given points (2,5) and (8,-3) and write the equation​
max2010maxim [7]

Answer:

Slope = \frac{-4}{3}

4x + 3y = 23

Step-by-step explanation:

slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-3-5}{8-2} =\frac{-8}{6} =\frac{-4}{3}

The equation:

\frac{y-y_{1} }{x-x_{1} }=m   m is the slope

y-y_{1}=m(x-x_{1} )

y - 5 = -4/3 (x - 2) Multiply both sides by 3

3y -15 = -4 (x - 2)  

3y - 15 = -4x + 8

3y + 4x = 8 + 15

3y + 4x = 23

4x + 3y = 23

7 0
3 years ago
What is the solution to -4x+12&lt;36?<br><br> A- x&lt;-6<br> B- x&gt;-6<br> C- x&gt;6<br> D-x&lt;6
Karolina [17]

Answer:

B- x > -6

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

Step-by-step explanation:

<u>Step 1: Define</u>

-4x + 12 < 36

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. [Subtraction Property of Equality] Subtract 12 on both sides:                       -4x < 24
  2. [Division Property of Equality] Divide -4 on both sides:                                x > -6
3 0
3 years ago
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