sqrt(2x-7)=x-7
We will consider each side of the equation as different functions. Let's press the Y= button and type the functions in different rows.
Having written the functions, push the WINDOW button and change the settings of the viewing window.
We can now push GRAPH to draw the functions.
b We have drawn the graphs of two functions using a graphing calculator in Part A. We will now sketch what is shown on the screen of the calculator. Let's examine the graphs on the screen.
We have the graphs of the functions y=sqrt(2x-7) and y=x-7 on the screen. Let's first make a table of values for the function y=sqrt(2x-7).
x
sqrt(2x-7)
y
3.5
sqrt(2( 3.5)-7)
0
8
sqrt(2( 8)-7)
3
Notice that the equation y=sqrt(2x-7) is a radical equation. As we can see from the screen and the table, the x-intercept of the function is 3.5 and the function also passes through the point (8,3). With this information, we will sketch the graph of the function.
Let's now make a table of values for the function y=x-7.
x
x-7
y
0
0-7
- 7
7
7-7
0
Both the calculator and the table show that the x- intercept and the y- intercept of the function y=x-7 are 7 and - 7, respectively. Considering this information, we will sketch the graph of the function on the same coordinate plane.
c We will now find the intersection point of the functions. To find it push 2nd, TRACE, and choose the fifth option, intersect.
The x-value of the intersection point of the two graphs is about 10.83, and its y-value is about 3.83.
d Finally, we will solve the given equation algebraically. To do this we will start by squaring both side of the equation.
We obtained a quadratic equation. Let's recall the Quadratic Formula used to find the solution(s) to quadratic equations.
ax^2+ bx+ c=0 [0.5em] ⇕ [0.5em] x=- b± sqrt(b^2-4 a c)/2 aTo solve our equation we first need to identify the values of a, b, and c.
x^2-16x+56=0 [0.5em] ⇕ [0.5em] 1x^2+( - 16)t+ 56=0
We see that a= 1, b= - 16, and c= 56. Let's substitute these values into the Quadratic Formula.
We will now check our solutions in the original equation. Let's first substitute 10.83 for x into the equation and check if it results in a true statement.
Notice that 5.17 does not satisfy the original equation. Therefore, the solution to the given equation is about 10.83, which is the same as the solution we got using the graphic calculator.
