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Correct! You can tell because the x² in your equation reveals that it is, in fact, a parabola.

Now, I’ll just start off by giving you an idea of how your graph might look like.

A parabola will give you a graph that will have somewhat of a U shape. The U will either concave upwards (a regular U shape) or concave downwards (an upside-down U shape).

The fact that the x² has a negative in front of it will confirm that your graph will be an upside-down U.

(If it had a regular U shape, x² would be positive)

Now, let’s solve for y :)

Solving for y is simple (in some cases). For each value of x, simply plug in the value into your equation, combine all terms together, and then you get y.

Let’s start with x= -3.

In order to solve for y, just plug in -3 wherever you find an x in your equation, and then solve.

The equation:

y=-x²-2x+3

How it looks like after you plug in -3:

y=-(-3)²-2(-3)+3

Solve for y and you get 0.

Try the rest out. You’ll find it very simple.

Hope this helped! :D

y = -x² - 2x + 3

If x = -3, then y = 0

If x = -2, then y = 3

If x = -1, then y = 4

If x = 0, then y = 3

If x = 1, then y = 0

If x = 2, then y = -5

=>

x= -3, -2, -1, 0, 1 and, 2

then ( just plug in)

y = -(-3)^2 - 2(-3) + 3 = -9+6+3=0

the rest you can do same way

y= 0, 3, 4, 3, 0, and -5

x = –3, y = –(–3)² – 2(–3) + 3 = –9 + 6 + 3 = 0

x = –2, y = –(–2)² – 2(–2) + 3 = –4 + 4 + 3 = 3

x = –1, y = –(–1)² – 2(–1) + 3 = –1 + 2 + 3 = 4

x = 0, y = –(0)² – 2(0) + 3 = 3

x = 1, y = –(1)² – 2(1) + 3 = –1 – 2 + 3 = 0

x = 2, y = –(2)² – 2(2) + 3 = –4 – 4 + 3 = –5

Please see my graph at the link below

https://www.desmos.com/calculator/guqdf2ccfg