Find the vertex of this parabola y=-4x^2-8x-7

(-1, -3)

Step-by-step explanation:

The standard form of a quadratic function is  

y = ax² + bx + c

The vertex form is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

In the equation y= -4x² - 8x -7

a = -4; b = -8; c = -7

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Calculate h

h = -(-8)/[2(-4)]

h = 8/(-8)

h = -1

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Calculate k

k = -4(-1)² -8(-1) -7

k = -4 +8 -7

k = -3

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The vertex is at (-1, -3).

The graph is an inverted parabola with its vertex at (-1, -3).

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,