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- 4x -3

A. Find the vertex by completing the square.
B. Find the y-intercept by setting x to 0.
C. Find the x-intercepts by setting y to 0.
D. Plot the vertex, y-intercept, and x-intercepts.

Answer 1

To graph the quadratic function, complete the square to find the vertex (-2, 1), set x to 0 to find the y-intercept (0, -3), and set y to 0 to find the x-intercepts, which in this case would be complex numbers.

Step-by-step explanation:

The question involves graphing a quadratic function by completing the square to find the vertex, finding the y-intercept by setting x to 0, and finding the x-intercepts by setting y to 0. Since the function was not properly provided, I will assume the function is y = -x^2 - 4x - 3.

1. Find the vertex by completing the square:
2. To complete the square for the quadratic function
3. y = -x^2 - 4x - 3
4. , first factor out the leading coefficient from the x-terms:
5. y = -(x^2 + 4x) - 3
6. Add and subtract the square of half the coefficient of x inside the parenthesis:
7. y = -(x^2 + 4x + 4 - 4) - 3
8. y = -(x + 2)^2 + 1
9. The vertex is at the point (-2, 1).
10. Find the y-intercept by setting x to 0:
11. y = -0^2 - 4(0) - 3
12. =>
13. y = -3
14. The y-intercept is at the point (0, -3).
15. Find the x-intercepts by setting y to 0:
16. To find the x-intercepts, solve the equation
17. 0 = -x^2 - 4x - 3
18. .
19. Since the quadratic does not factor neatly, you can use the Quadratic Formula. In this case, the x-intercepts will be complex since the discriminant is negative.
20. Plot the vertex, y-intercept, and x-intercepts on the graph paper (provided by the student).