Fill out the information below for the following graph of a quadratic function. Please Help!!

Please refer to the images attached below.

Step-by-step explanation:

Quadratic Functions are functions of degree 2. The graph of any quadratic function is a parabola that has a vertex and axis of symmetry.

Some Properties of Graph Translations

1. y=a(x-h)^2+ky=a(x−h)

2

+k

This means that the new function is translated h units to the right and k units going up.

2. y=a(x-h)^2-ky=a(x−h)

2

−k

This means that the new function is translated h units to the right and k units going down.

3. y=a(x+h)^2+ky=a(x+h)

2

+k

This means that the new function is translated h units to the left and k units going up.

4. y=a(x+h)^2-ky=a(x+h)

2

−k

This means that the new function is translated h units to the left and k units going down.

First, let's graph the function y=3x^2+3y=3x

2

+3 . The vertex is at the point (0,3)(0,3) . Please refer to Figure 1 below.

Now, start from the vertex of the first function, (0,3)(0,3) , as you notice that the function y=3(x-3)^2+1y=3(x−3)

2

+1 is 3 units translation to right and one unit translation going up. This means that the new vertex is the point (3,1)(3,1) .Please refer to Figure 2.

For the function, y=3(x+3)^2-1y=3(x+3)

2

−1 , start from the vertex of the first function, (0,3)(0,3) , then make a translation of 3 units to the left and a translation of 1 unit down. This gives us a new vertex of (-1, -3)(−1,−3) . Please refer to Figure 3.

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Step-by-step explanation:

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4