# Jackie Is Analyzing A Quadratic Function F(x) And A Linear Function G(x). Will They Intersect?

Consider the quadratic function and the linear function g(x) defined as

No, they do not intersect Walkthrough: We have an expression for the function f(x) in the form: and the array of values ​​for g(x) is given in the form: xg(x) 1−1 2− 2 3−3 or i.e. the function is given by: We can also find the equation of g(x) by the slope-intercept form, i.e. say Here When x=1 y=-1 it means -1=m+c—–(1) And when x=2 y=-2 -2=2m+c——(2) By solving the two equations below above, i.e. eqn(1) and (2) by the method of elimination, we have: m=-1 and c =0 Therefore, from the graph of f(x) and g( x), we can clearly see that the graph of two functions does not intersect at any point in the coordinate plane. Therefore, the last option is correct. No, they will not meet.

Yes, the functions intersect at the points (0,2) and (9,583,47,913). Walkthrough: We have the functions, f of x equals half x squared plus 2 i and g(x) given by the table. The general form of a linear function is y=mx+b, where m is the slope and b is the intercept. We will find the slope of the function g(x), using , we get, i.e. m= 5. Thus, substituting (1,5) into y=5x+b ⇒ 5 = 5×1 +b ⇒ b= 0. Thus, the equation of g(x) is y= 5x. After plotting the function f(x) and g(x), we get the following graph. From the graph, we see that the functions intersect at the points (0,2) and (9,583,47,913).

Therefore, they will intersect in positive x coordinates. Walkthrough: We have two functions f(x) and g(x) as: and . As the table of values ​​of g is given as follows: xg(x) 1 5 2 10 3 15 thus solving for g(x) using the colon. Let g(x)=y We use the slope-intercept form as follows: y=mx+c where m is the slope of the line and c is the intercept of the line. now for x=1 ,y=5 5=m+c and for x=2, y=10 10=2m+c by solving the two equations above using the method of elimination, we have: m=5 and c=0 So , g (x)=5x Now we can see by solving the equation f(x)=g(x), i.e. by solving a quadratic equation formed by the equation of f(x) and g(x) that the graph intersects at x=0, 4174 ex=9.5826. (since solving and therefore solving this quadratic equation). Therefore, they will intersect in positive x coordinates.

If we substitute 13 for f(x) and get a value for x, the two equations will intersect. So f(x) = x^2 + 6x +1013 = x^2 + 6x+ 10x^2 + 6x – 3 = 0 Solving quadratic equations: The roots of the equation are x = 0.4641 and x = – 6.4541 Therefore, the line will intersect the quadratic function.

the answer is (a) Walkthrough: I just did it

They will not meet.

Yes, the functions intersect at the points (0,2) and (9,583,47,913). Walkthrough: We have the functions, f of x equals half x squared plus 2 i and g(x) given by the table. The general form of a linear function is y=mx+b, where m is the slope and b is the intercept. We will find the slope of the function g(x), using , we get, i.e. m= 5. Thus, substituting (1,5) into y=5x+b ⇒ 5 = 5×1 +b ⇒ b= 0. Thus, the equation of g(x) is y= 5x. After plotting the function f(x) and g(x), we get the following graph. From the graph, we see that the functions intersect at the points (0,2) and (9,583,47,913).

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