In this diagram, ABAC – AEDF. If the area of ABAC = 15 in?, what is the
area of AEDF?
D
E
4 in
F
F
B
5 in
С
Area = [?] in2

Area of ∆EDF = 9.6 in.²

Step-by-step explanation:

Given:

∆BAC ~ ∆EDF

Area of ∆BAC = 15 in.²

EF = 4 in.

BC = 5 in.

Required:

Area of ∆EDF

SOLUTION:

The ratio of the area of two similar shape = the ratio of the square of their corresponding side lengths

Let x represent the area of ∆EDF

Therefore:

15/x = 5²/4²

15/x = 25/16

Cross multiply

x×25 = 15×16

25x = 240

Divide both sides by 25

x = 240/25

x = 9.6

Area of ∆EDF = 9.6 in.²

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

answer: 2530

hope this