Question

In the box, complete the first 4 steps for graphing the quadratic function given. (Use ^ on the keyboard to indicate an exponent.) Then print a sheet of graph paper and graph the quadratic function to turn in to your teacher. Be sure to label the axes and vertex.
y = -x 2 - 4x - 3

Answer 1

Step 1: convert the equation into fhe vertex form

To do you can complete squares:

y = - [x^2 + 4x + 3]

y = - [ (x + 2)^2 - 4 + 3]

y = - [ (x + 2)^2 - 1] = - (x+2)^2 + 1

Then the vertex is (-2, 1)

Now you can drasw the vertex


Step 2: Find the roots (zeros)

y = - [ (x + 2)^2 - 1] = 0

(x + 2)^2 - 1 = 0

(x+2)^2 = 1

(x+2) = (+/-) √1

x + 2 = (+/-1)

x = - 2 +/- 1

x = -1 and x = -3

Now you draw the points (-1,0) , (-3,0)

Step 3: find the interception with the y-axis.

That is y value when x = 0

y = - (0)^2 - 4(0) - 3 = -3

Then draw the point (0, -3)

Step 4: given that the coefficent of x is negative (-1) the parabola is open downward.

So, with those four points: vertex (-2,1), (-1,0), (-3,0) and (0,-3), you can sketch the function.