Solve 3x^2-8x+4=0 by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.
A)2;between 0 and 1
B)between 0 and 1;between 7 and 8
C)1,2
D)between 0 and 1;between 3 and 4
I don't understand this one either its gotta be A or C I don't undertand what I got from a website which gave me X1=2 and X2=.6 repeating
let y = 3x^2-8x+4 or f(x) = 3x^2-8x+4 , same thing
try a few x's
I tried -1,0,1,2,3 and y values of
15,4,-1,0,7
notice when x = 0 the graph is above the x-axis, but when x=1 the graph is below the x-axis.
So there has to be a solution between x=0 and x=1
Also notice when x=2 , y =0, so x=2 is a solution.
Solutions to equations are where the matching graph cuts the x-axis.
Now that we know that we have an exact solution at x=2, x-2 must be an exact factror, and sure enough
3x^2-8x+4 = (x-2)(3x-2)
so x=2 or x=2/3
So C would be the choice?
NOOO, it is A
Did you not read when I said:
"notice when x = 0 the graph is above the x-axis, but when x=1 the graph is below the x-axis.
So there has to be a solution between x=0 and x=1
Also notice when x=2 , y =0, so x=2 is a solution. "
Oh yeah duh. my mistake
To solve the quadratic equation 3x^2 - 8x + 4 = 0 by graphing, follow these steps:
1. Plot the equation on a graph (either by hand or using a graphing calculator).
The equation is in the form of Ax^2 + Bx + C = 0, where A = 3, B = -8, and C = 4.
2. The graph will be a parabola that opens upwards because the coefficient of the x^2 term (A) is positive.
3. Use the graph to determine the solutions or roots of the equation. The solutions are the x-intercepts or the points where the graph intersects the x-axis. These points represent the values of x when y = 0.
Looking at the graph, it seems that there are two x-intercepts.
Now let's examine the options provided:
A) 2; between 0 and 1 - This option suggests the equation has a root at x = 2, which does not seem to be the case based on the graph, so we can eliminate this option.
B) Between 0 and 1; between 7 and 8 - This option suggests that the roots are between 0 and 1 and also between 7 and 8. Since we can see two x-intercepts on the graph between approximately 0 and 1, this option seems plausible.
C) 1, 2 - This option suggests that the roots are precisely at x = 1 and x = 2. Looking at the graph, we do observe that the parabola intersects the x-axis around these values. Thus, this option is also plausible.
D) Between 0 and 1; between 3 and 4 - This option suggests that the roots are between 0 and 1 and also between 3 and 4. Looking at the graph, we can see one x-intercept between approximately 0 and 1, but there isn't any apparent x-intercept between 3 and 4. Therefore, this option does not seem accurate.
Based on the graph, options B and C seem plausible. However, since the graph is not precise, it is difficult to determine the exact values of the roots. It's also worth mentioning that the website you refer to suggests x1 = 2 and x2 = 0.6 repeating, which aligns with option C.
Therefore, the answer would be: C) 1, 2