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vlabodo [156]
3 years ago
12

a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the

equation of the parabola.
Mathematics
1 answer:
nlexa [21]3 years ago
7 0

Answer:

The standard equation of the parabola is:

y=-\frac{3}{2}x^2+12x-18

Step-by-step explanation:

An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.

We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.

y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2

Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:

y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}

Then the equation of the parabola becomes:

y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18

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vladimir2022 [97]

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5 0
3 years ago
What is a triangle equal to​
VashaNatasha [74]

Answer:

A triangle equals 180 degrees.

4 0
3 years ago
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Lyrx [107]

Answer:

Let x rep the lenght of the shorter one

Then the longer one is 2x+1

Therefore

(2x+1) + x = 16

We now solve for x

2x + 1 + x = 16

Group and evaluate like terms

3x +1 = 16

3x = 16 -1

× = 15/3

x = 5

So the shorter one is 5 ft

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4 0
3 years ago
A woman spent two thirds of her money she lost two thirds the remainder and then had $4 left how much money did she start with
Lisa [10]

Answer

Find out  how much money did she start with.

To proof

let us assume that the money she had be x.

As given

woman spent two thirds of her money

Money\ spent = \frac{2x}{3}

Money she had after spent two thirds of her money  = Total money - money spent

= x - \frac{2x}{3}

= \frac{1x}{3}

As given she lost two thirds the remainder

=\frac{2}{3}\times ( money\ she\ had\ after\ spending\ two\ thirds\ of\ her\ money)

= \frac{2}{3} \times\frac{1x}{3}

we get

=\frac{2x}{9}

Money she had after lost two thirds the remainder = Money she had after spent two thirds of her money - she lost two thirds the remainder

= \frac{1x}{3} - \frac{2x}{9}

= \frac{1x}{9}

As given

she had $4 left

thus

\frac{1x}{9} = 4

x = $36

she start with $36.

Hence proved

3 0
3 years ago
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The car show sold the same number of general admission tickets as student discount tickets. The student tickets cost $6.00 less
DIA [1.3K]

Answer:

$15.00

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3000-1800

1200

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200

3000/200

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