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Answer:
see below
Step-by-step explanation:
f(x) = 4x^2 + 8x − 5
To find the x intercepts set y = 0
0 =4x^2 + 8x − 5
Factor
0=(2x-1)(2x+5)
Using the zero product property
2x-1 =0 2x+5 =0
2x=1 2x = -5
x = 1/2 x = -5/2
The x intercepts are ( 1/2 ,0) and ( -5/2,0)
Rewriting in vertex form by completing the square
4 ( x^2 + 2x) -5
4 ( x^2+2x +1) -4*1 -5
4 ( x+1) ^2 -9
Vertex form is
a( x-h) ^2 +k where ( h,k) is the vertex
The vertex is ( -1,-9)
We know it opens upwards since a > 0
Plot the vertex and the x intercepts
The graph is symmetric on based on the vertex
Answer:
203 feet.
Step-by-step explanation:
Please find the attachment.
Let h represent the height of the building.
We have been given that at 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal.
We know that tangent relates opposite side of a right triangle to its adjacent side.
Upon substituting our given values in above formula, we will get:
Therefore, the building is approximately 203 feet high.
