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

Question

asked Apr 5, 2020 55.2k views

1 Answer

Tofro · Answer 1 · 2020-04-10T15:02:49+0000

Answer:

$y\leq 4$

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
$y\leq 4$