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remotecontrolbrain

I would start with the quadratic form:

y = a*(x-b) + c

we need to determine (a,b,c)

from the graph we know two points: (-3,4) and (-2,2)

b stands for the horizontal offset and that is -3 in this case so b=-3

c stands for vertical offset, in this case c = 4

so what's left:

y = a(x+3)^2 + 4

Plug in the point (-2,2):

2 = a(-2+3) + 4 = a + 4 ==> a = -2

so the equation we looked for is:

y = -2(x+3)^2 + 4

MrRoyal

A parabola is represented as: [tex]\mathbf{y= a(x - h)^2 + k}[/tex]

The equation of the parabola is: [tex]\mathbf{y = -\frac{2}{25}(x -3)^2 + 4}[/tex]

From the graph, we have:

[tex]\mathbf{(x,y) = (-2,2)}[/tex] --- a point on the graph

[tex]\mathbf{(h,k) = (3,4)}[/tex] --- the vertex of the graph

Substitute these values in [tex]\mathbf{y= a(x - h)^2 + k}[/tex]

[tex]\mathbf{2 = a(-2 - 3)^2 + 4}[/tex]

[tex]\mathbf{2 = a(-5)^2 + 4}[/tex]

[tex]\mathbf{2 = 25a + 4}[/tex]

Subtract 4 from both sides

[tex]\mathbf{25a=-2}[/tex]

Divide both sides by 25

[tex]\mathbf{a=-\frac{2}{25}}[/tex]

Substitute [tex]\mathbf{a=-\frac{2}{25}}[/tex] and [tex]\mathbf{(h,k) = (3,4)}[/tex] in [tex]\mathbf{y= a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -\frac{2}{25}(x -3)^2 + 4}[/tex]

Hence, the equation of the parabola is: [tex]\mathbf{y = -\frac{2}{25}(x -3)^2 + 4}[/tex]

Read more about equations of parabola at:

https://brainly.com/question/4074088

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