Question

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

Answer 1

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 $y\leq 4$