Pertanyaan
15. Nilai diskriminan dari persamaan kuadrat 2x^2-2x+6=0 adalah __ a. - -44 b. -22 C. 11 d. 22 16. Grafik fungsi kuadrat f(x)=4x^2-4x-2 memotong sumbu Y di titik __ a. . (0,2) b. (0,-2) C. (2,0) d. (-2,0) 17. Sumbu simetri grafik fungsi kuadrat f(x)=-x^2+ 8x-12 adalah __ a. x=8 b. x=4 C. x=-4 d. x=-8 18. Titi k maksimum grafik fungsi kuadra f(x)=-x^2+6x-4 adalah __ a. . (3,23) b. (3,8) C. (3,5) d. (3,1)
Solusi
Jawaban
15. a. -44, 16. b. (0,-2), 17. b. x=4, 18. c. (3,5)
Penjelasan
15. The discriminant of a quadratic equation is calculated using the formula D = b^2 - 4ac. For the given equation 2x^2 - 2x + 6 = 0, a = 2, b = -2, and c = 6. Substituting these values into the formula gives D = (-2)^2 - 4*2*6 = 4 - 48 = -44. 16. The graph of a quadratic function f(x) = ax^2 + bx + c intersects the y-axis at the point where x = 0. Substituting x = 0 into the given function f(x) = 4x^2 - 4x - 2 gives f(0) = 4*0^2 - 4*0 - 2 = -2. Therefore, the intersection point with the y-axis is (0, -2). 17. The axis of symmetry of a quadratic function f(x) = ax^2 + bx + c is given by the line x = -b/2a. For the given function f(x) = -x^2 + 8x - 12, a = -1 and b = 8. Therefore, the axis of symmetry is x = -8/(2*-1) = 4. 18. The maximum point of a quadratic function f(x) = ax^2 + bx + c occurs at x = -b/2a. For the given function f(x) = -x^2 + 6x - 4, a = -1 and b = 6. Therefore, the x-coordinate of the maximum point is x = -6/(2*-1) = 3. Substituting x = 3 into the function gives f(3) = -(3)^2 + 6*3 - 4 = -9 + 18 - 4 = 5. Therefore, the maximum point is (3, 5).