Answer:
is
or
Explanation:
A) To generate the table of values, we can substitute different values of x into the equation and solve for y.
x y
-2 26
-1 12
0 4
1 2
2 10
To plot the graph of the function, we can use the table of values and plot the corresponding points on a graph with a scale of 4 for the y-axis and 2cm to 1 unit along the x-axis. The graph should look like a parabola opening upwards.
c) To solve for the root of the equation 4-5x+3x^2=0, we can use the graph and find the x-coordinate of the point where the graph intersects the x-axis. This point is also known as the x-intercept or the root of the equation. From the graph, we can see that the root is approximately x=0.83.
To solve the equation 3x^2 -5x=2, we can rearrange it to the form 3x^2 -5x-2=0 and factor it as (3x+1)(x-2)=0. This gives us two solutions: x=-1/3 and x=2.
To determine the range of values of x for which 35x<4-5x+3x^2, we can rearrange the inequality to the form 3x^2-40x+4>0 and factor it as (3x-1)(x-4/3)>0. This means that either (3x-1) and (x-4/3) are both positive or both negative.
When (3x-1)>0 and (x-4/3)>0, we get x>1/3 and x>4/3, which means x>4/3.
When (3x-1)<0 and (x-4/3)<0, we get x<1/3 and x<4/3, which means x<1/3.
Therefore, the range of values of x for which 35x<4-5x+3x^2 is x<1/3 or x>4/3.