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Ray Of Light [21]
3 years ago
14

The vertex if the parabola below is at the point (2,4) and the point (3,6) is on the parabola. What is the equations the parabol

a
Mathematics
2 answers:
Sloan [31]3 years ago
4 0
I think the equation is 2(x-2)^2+4
3241004551 [841]3 years ago
4 0

Answer:

y = 2(x-2)^2+4  is the equations the parabola

Step-by-step explanation:

The standard equation of parabola is given by:

y = a(x-h)^2+k           ....[1]

where,

a is the non zero real number and

(h, k) is the vertex of the parabola.

As per the statement:

The vertex if the parabola below is at the point (2,4)

⇒(h, k) = (2, 4)

⇒h =2 and k =4

Substitute these in [1] we have;

y = a(x-2)^2+4

Since, the point (3,6) is on the parabola

⇒x = 3 and y = 6

then;

6 = a(3-2)^2+4

6 = a+4

Subtract 4 from both sides we have:

2= a

or

a = 2

⇒y = 2(x-2)^2+4

Therefore, the equations the parabola is, y = 2(x-2)^2+4

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kiruha [24]

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Here, since we want our ratio in simplest form,

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3 years ago
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Maksim231197 [3]

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5 0
3 years ago
Explain the procedure (but don't create the graph) for graphing the quadratic function in factored form f(x) = (x - 2)(x + 4) us
hichkok12 [17]

Answer:  You will need to find the x-intercepts and the vertex

Step-by-step explanation: Use the information in the factors and some formulae.

The x- intercepts are the points where the parabola crosses the x-axis. The x-axis is where y = 0

Set each factor equal to 0 and solve:

x-2=0, so x = +2 and x +4 = 0, so x = -4    (you would plot these if creating the graph)

To find the vertex you need the Vertex Formula: x = -b/2a

b is the coefficient of the x term in the middle of the quadratic equation; you can just do the O and I parts of FOIL to get b:  -2x + 4x = 2x  You know a = 1 because x²  will have the implied (missing)(1).

Put the numbers in the Formula: x = -b/2a   x = -(2)/2(1)  -2/2 = -1  

-1 is the "x-value" of the vertex.  

The y value is the 'c' in the quadratic formula. You get that from the  L part of FOIL   -2 × 4 = -8 .

So, your coordinates for the vertex:  ( -1, -8 )

If you were creating a graph, you would plot that point, then draw the parabola starting there and through the x-intercepts.  

5 0
3 years ago
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