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Nimfa-mama [501]
3 years ago
10

The area of triangle formed by points of intersection of parabola y=a(x+5)(x−1) with the coordinate axes is 12. Find a if it is

known that parabola opens upward.

Mathematics
1 answer:
garri49 [273]3 years ago
8 0
ANSWER


a = \frac{4}{5}


EXPLANATION

The given parabola has equation,

y = a(x + 5)(x - 1)

The y-intercept is

y = a(0+ 5)(0- 1)

y = - 5a

This gives one vertex of the triangle to be,

(0,-5a)

The x-intercept is

a(x + 5)(x - 1) = 0

This implies

(x + 5)(x - 1) = 0

(x + 5) = 0 \: or \: (x - 1) = 0

x = - 5 \: or \: x = 1

The other two vertices of the triangle is,

(-5,0),(1,0)

The height of this triangle is

h = 5a

Area= \frac{1}{2} \times base \times height

12= \frac{1}{2} \times 6 \times 5a

12 = 15a

a = \frac{12}{15}

a = \frac{4}{5}

Since

a > \: 0
it means the parabola opens upwards.

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