Question

I need help with this one also

Answer 1

To graph the first equation, the parabola, you must find the zeros.

This can be accomplished by setting the equation equal to zero and factoring:

0= x² +4x + 3

(x+3) (x+1)

zeros = -3, -1

These zeros are the x - intercepts in your graph.

The 3 in your equation is the y intercept

Now, find the vertex. The vertex formula is
`(-b)/(2a)` where x² +4x + 3 follows the quadratic format of ax² +bx + c

Rewrite the formula by plugging in a=1 and b=4:
`(-4)/(2 (1))` = -2

This give you the x coordinate of your vertex. Now plug -2 as x to find the y coordinate: (-2)² +4(-2) + 3 = -1

Your vertex is (-2, -1)

Now use your information to draw a parabola. The graph should look like the one attached.

Now for the second equation. The second equation is a linear equation that follows the mx + b = y format, where m is the slope and b is the y intercept.

`(1)/(2)` = slope

1 = y intercept

Starting at the y intercept, move up 1 unit and over 2 units. Continue to do this until you have a diagonal line. Your graph should look like the one attached.

For your last question, f(x) will always equal g(x) wherever the two graphs intersect. This happens on the point (0,1)