x = 9/2 or x = -2 Solved by using the quadratic equation formula.
The solutions work out as: x = 52/11, y = 101/11 and x = -2, y = -11
The product of the roots of the equation 2x2 -x -2 = 2 is 2x2 -x -2 = 2.
y = 2x2 + 3x + 6 Since a > 0 (a = 2, b = 3, c = 6) the graph opens upward. The coordinates of the vertex are (-b/2a, f(-b/2a)) = (- 0.75, 4.875). The equation of the axis of symmetry is x = -0.75.
Differentiate the function with respect to x: d/dx (x3 - 2x2 - 5x + 6) = 3x2 - 4x - 5 Set this derivative = 0 and solve. 3x2 - 4x - 5 = 0 implies that x = -0.7863 or 2.1196 (to 4 dp)
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y=2x2+5. Plug in 0 for x, and you get y=2(0)^2 +5 =0+5=5. 5 is the minimum value for y.
2x2 + 3x - 20 = (x + 4)(2x - 5).
Assuming the missing symbol there is an equals sign, then we have: y - 2x2 - 4x = 4 We can find it's vertex very easily by solving for y, and finding where it's derivative equals zero: y = 2x2 + 4x + 4 y' = 4x + 4 0 = 4x + 4 x = -1 So the vertex occurs Where x = -1. Now we can plug that back into the original equation to find y: y = 2x2 + 4x + 4 y = 2 - 4 + 4 y = 2 So the vertex is at the point (-1, 2)
-5
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1.249 radians from the horizontal.
x = 9/2 or x = -2 Solved by using the quadratic equation formula.
= Z X and Y are examples. 2 to the power of X multiplied by 2 to the power 2 equals 16 What is X? X=2 2 to the power of 2 (2x2) multiplied (X) by 2 to the power of 2 (2x2) (2x2)4 X (2x2)4 = 4X4 = 16
y = 2x2 - 3x - 20 ∴ y = 2x2 - 8x + 5x - 20 ∴ y = 2x(x - 4) + 5(x - 4) ∴ y = (2x + 5)(x - 4) The x intercepts occur when y = 0, which happens when either of the two factors on the left side of the equation equal zero. This means that they are at the points (-5/2, 0) and (4, 0).