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SVEN [57.7K]
3 years ago
6

5 What is the range of y = -x2 - 2x + 3? Ax<4 B x2-4 c y<4 Dy2-4

Mathematics
1 answer:
Vesnalui [34]3 years ago
7 0

Answer:

y\leq 4

Step-by-step explanation:

we have

y=-x^{2}-2x+3

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex is a maximum

The vertex is the point (h,k)

The range of the function is the interval (-∞,k]

so

y\leq k

Convert the quadratic equation in vertex form

Factor -1 leading coefficient

y=-(x^{2}+2x)+3

Complete the square

y=-(x^{2}+2x+1)+3+1

y=-(x^{2}+2x+1)+4

Rewrite as perfect squares

y=-(x+1)^{2}+4

The vertex is the point (-1,4)

therefore

The range is y\leq 4

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x ≥ 1.52 / 3 x - 1 = 2 / 3 x + 4⇒ -1 = 4 which is not possible .Now for all x ≤ 1.5- 2 /3 x + 1 = 2 / 3 x + 4⇒ 4 / 3 x = -3  x = - 9 /4 Hence absolute value = - 9 / 3 .

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