# math

posted by .

determine the value of k such that g(x)=3x+k intersects the quadratic function f(x)=2x^2-5x+3 at exactly one point

determine the value(s) of k such that the linear function g(x)=4x+k does not intersect the parabola f(x)=-3x^2-x+4

• math -

2x^2 - 5x + 3 = 3x + k
2x^2 - 8x + (3-k) = 0

We want both roots of this to be the same. That is, it must be a perfect square.

2(x-2)^2 = 2x^2 - 8x + 8

So, we want 3-k=8 or k=-5

SO, 3x-5 intersects the parabola in exactly one point.

-----------

If the line does not intersect the parabola, then f(x)-g(x) = 0 must have a negative discriminant.

The line intersects the parabola when

4x+k = -3x^2 - x + 4
3x^2 + 5x + k-4 = 0

5^2 - 4(3)(k-4) = 25 - 12k + 48 = 73 - 12k < 0

73-12k < 0
k > 73/12

## Similar Questions

1. ### discrete math

1. let A and B be sets. Show that A U (B - A)=A U B 2. determine whether f is a function from Z to R if a) f(n)= +n b) 1/(n square -4) For 1. B-A is the same as B intersect ~A (That's the complement of A) So A U B = A U (B int ~A) …
2. ### math

How do I know that x^2-7=y is a function?
3. ### Need Help!! Algebra

I am having trouble in this class and need help with this question.. What similarities and differences do you see between functions and linear equations studied Are all linear equations functions?
4. ### Calculus AB

Analyze the function ln x=cx^2 to find the unique value of c such that there is exactly one solution to the equation. To do this find the value of c such that both sides of the equation have equivalent slopes at some point; this will …
5. ### calc

analyze the function ln x = cx^2 to find the unique value of c such that there is exactly one solution to the equation. to do this, find the value of c such that both sides of the equation have equivalent slopes at some point; this …
6. ### Calculus

Let f be a twice-differentiable function such that f(2)=5 and f(5)=2. Let g be the function given by g(x)= f(f(x)). (a) Explain why there must be a value c for 2 < c < 5 such that f'(c) = -1. (b) Show that g' (2) = g' (5). Use …
7. ### Math

determine the value of k such that g(x)=3x+k intersects the quadratic function f(x)+2x^2-5x+3
8. ### Math Help!

A.) Determine "a" and "k" so both points are on the graph of the function. 1.) (0,1) (2,1); y=a(x-1)^2+k 2.) (1,11) (2,-19); y=a(x+1)^2+k B.) Determine whether or not the function f(x)=0.25(2x-15)^2+15 has a mazimum or a minimum value. …
9. ### Math

A quadratic function is defined by f(x)=-3.7x^2+6.8x+4.2. A linear function is defined by g(x)=-0.5x+k. Determine the value of k so that the line intersects the parabola at exactly one point. Write your answer to the nearest hundredth
10. ### Algebra

Two graph never intersect. As such, the equation has no solutions. Create an equation where the left side is a linear function and the right side is a square root function. Make it so that the equation has exactly one solution.

More Similar Questions