Question

1. Consider the following quadratic function y=4-5x+3x². a) b) c) Generate the table of values of the function for all x ranging from to Use the table to plot the graph of the function y = f(x) for all scale 4or the y-axis and 2cm to I unit along the x-axis. Using the graph: Solve for the root of the equation 4-5x+3x²=0. Solve the equation 3x² -5x=2. (iii) Determine the range of values of x for which 35x​

Answer 1

Answer:
`35x < 4-5x+3x^2` is
`x < (1)/(3)` or
`x > (4)/(3)`

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.