Complete parts a – c for each quadratic function:
a. Find the y-intercept, the equation of the axis of symmetry and the x-
coordinate of the vertex.
b. Make a table of values that
includes the vertex.
c. Use this information to graph the
function.
1. f(x) = 2x^2
2. f(x) = x^2 + 4
3. f(x) = 2x^2 – 4
4. f(x) = x^2 – 4x + 4
5. f(x) = x^2 – 4x – 5
6. f(x) = 3x^2 + 6x – 1
7. f(x) = -3x^2 – 4x
8. f(x) = 0.5x^2 – 1
9. f(x) = ½x^2 + 3x + 9/2
Determine whether each function has a maximum or a minimum value. Then find the maximum or minimum value of each function:
10. f(x) = 3x^2
11. f(x) = x^2 – 8x + 2
12. f(x) = 4x – x^2 + 1
13. f(x) = 2x + 2x^2 + 5
14. f(x) = -7 – 3x^2 + 12x
15. f(x) = -½x^2 – 2x + 3
Thank You!!
So what is your question?
This would be a piece of cake on a graphing calculator.
Thanks I didn't even think of that! I am however stuck on these problems, i know theres a lot though, any help would be great, but i can't seem to understand the complex numbers, thankyou!
Simplify:
1.SquareRoot(-144)
2.SquareRoot(-64x^4)
3.SquareRoot(-13)*SquareRoot(-26)
4.(-2i)(-6i)(4i)
5. i^13
6. i3^8
7.(5 – 2i) + (4 + 4i)
8.(3 – 4i) – (1 – 4i)
9.(3 + 4i)(3 – 4i)
10.(6 – 2i)(1 + i)
11. (4i)/(3+i)
12. (10+i)/(4-i)
13. (-5 + 2i)(6 – i)(4 + 3i)
14. (5-iSquareRoot(3))/(5-iSquareRoot(3))
15. Find the sum of ix2 – (2 + 3i)x + 2 and 4x2 + (5 + 2i)x – 4i.
Solve each equation:
16. 5x^2 + 5 = 0
17. 2x^2 + 12 = 0
18. -3x^2 – 9 = 0
19. (2/3)x^2 + 30 = 0
Find the values of m and n that make each equation true:
20. 8 + 15i = 2m + 3ni
21. (2m + 5) + (1 – n)i = -2 + 4i
22. (m + 2n) + (2m – n)i = 5 + 5i
a. To find the y-intercept, plug in x=0 into the quadratic function. The y-intercept is the value of f(x) when x=0.
b. To find the equation of the axis of symmetry, use the formula x = -b/2a, where a and b are the coefficients of the quadratic function.
c. To find the x-coordinate of the vertex, use the formula x = -b/2a. Plug in the x-coordinate into the quadratic function to find the y-coordinate of the vertex.
1. f(x) = 2x^2
a. The y-intercept: Plug in x=0, f(0) = 2(0)^2 = 0. Therefore, the y-intercept is (0,0).
b. The equation of the axis of symmetry: x = -b/2a = -0/(2*2) = 0. Therefore, the equation of the axis of symmetry is x = 0.
c. The x-coordinate of the vertex: x = -b/2a = -0/(2*2) = 0. Plug in x=0 into the quadratic function, f(0) = 2(0)^2 = 0. Therefore, the vertex is (0,0).
2. f(x) = x^2 + 4
a. The y-intercept: Plug in x=0, f(0) = (0)^2 + 4 = 4. Therefore, the y-intercept is (0,4).
b. The equation of the axis of symmetry: x = -b/2a = -0/(2*1) = 0. Therefore, the equation of the axis of symmetry is x = 0.
c. The x-coordinate of the vertex: x = -b/2a = -0/(2*1) = 0. Plug in x=0 into the quadratic function, f(0) = (0)^2 + 4 = 4. Therefore, the vertex is (0,4).