What is the area of the triangle formed by connecting the points where

Question

What is the area of the triangle formed by connecting the points where the parabola  y=2x^2-7x-4  intersects the  x  and  y -axes?

A) 6
B) 7
C) 8
D) 9
E) 10

CrackverbalGMAT · Answer

The roots of the equation 2 x^2  - 7x - 4 = 0 can be found by splitting the middle term into -8x and x

2 x^2  - 8x + x - 4 = 0
2x (x - 4) + 1(x - 4)
(2x + 1)(x - 4) = 0

x = - \frac{1}{2}  and 4 are the roots. The parabola cuts the x axis at these points (-0.5,0) and (4,0)

The y intercept can be found by putting x = 0 in the equation, 2 x^2  - 7x - 4 = 0
We get y = -4. The point at which the parabola cuts the y axis is (0, -4)

Refer to the figure below.

Area of the triangle =  \frac{1}{2}  * base * height

The area of  	riangle{ABC}  = area of  	riangle{AOB}  + area of  	riangle{OBC}

=  \frac{1}{2}  * 0.5 * 4 +  \frac{1}{2}  * 4 * 4 = 1 + 8 = 9

Option D

Arun Kumar

yashikaaggarwal · Answer

the equation y = 2x^2-7x-4 intersect both X and Y axis
When it intersect Y axis, X is equal to zero
y = 2x^2-7x-4
y = 2(0)^2-7(0)-4
y = -4

When it intersect x axis, y is equal to zero
y = 2x^2-7x-4
0 = 2x^2-7x-4
0 = 2x^2-8x+x-4
0 = 2x(x-4)+1(x-4)
0 = (x-4)(2x+1)
x = 4 and -1/2

plotting points on graph, we get triangle ABC
Area of triangle BOC = 1/2*4*4 = 8
Area of triangle AOC = 1/2*1/2*4 = 1
Area of ABC = Area of BOC + Area of AOC
Area of ABC = 8+1
Area of ABC = 9

Answer is D

ScottTargetTestPrep · Answer

Solution:

The point of the parabola on the y-axis is its y-intercept. To find it, we set x = 0 and solve for y:

y = 2(0)^2 - 7(0) - 4 = -4

Therefore, the y-intercept is -4.

Similarly, the points of the parabola on the x-axis are its x-intercepts. To find them, we set y = 0 and solve for x:

0 = 2x^2 - 7 - 4

0 = (2x + 1)(x - 4)

x = -1/2 or x = 4

Therefore, the x-intercepts are -1/2 and 4.

By connecting the x- and y-intercepts, we have a triangle whose base is on the x-axis with length 4 - (-1/2) = 9/2 and whose height is on the y-axis with length |-4| = 4. Therefore, the area of the triangle is 1/2 x 9/2 x 4 = 9.

Answer: D

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What is the area of the triangle formed by connecting the points where

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What is the area of the triangle formed by connecting the points where

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