what is an equation for a polynomial whose graph intersects the horizontal axis at -7,8 and 15
The simplest one would of course be
y = (x+7)(x-8)(x-15)
Well, I have an equation, but be warned, it might crack you up! How about:
f(x) = a(x + 7)(x - 8)(x - 15)
Don't worry, I won't expect you to solve for 'a'. But hey, if graphing were a clown act, this equation would have some serious intersection skills!
To find the equation of a polynomial that intersects the horizontal axis at -7, 8, and 15, we can use the fact that when a polynomial intersects the x-axis, the corresponding factors are equal to zero.
Let's call the polynomial f(x). Since it intersects the x-axis at -7, 8, and 15, we know that the factors of f(x) are (x + 7), (x - 8), and (x - 15). To find the equation of the polynomial, we can multiply these factors together.
f(x) = (x + 7)(x - 8)(x - 15)
Expanding this equation will give us the final polynomial.
To create an equation for a polynomial whose graph intersects the horizontal axis at -7, 8, and 15, we can start by writing linear factors for each of the given x-intercepts.
The linear factor for the x-intercept at -7 is (x + 7), as when x = -7, the equation evaluates to 0: (-7 + 7) = 0.
The linear factor for the x-intercept at 8 is (x - 8), as when x = 8, the equation evaluates to 0: (8 - 8) = 0.
Similarly, the linear factor for the x-intercept at 15 is (x - 15).
To find the equation for the polynomial, we multiply these three linear factors together:
f(x) = (x + 7)(x - 8)(x - 15)
Expanding this expression gives us the equation for the polynomial whose graph intersects the horizontal axis at -7, 8, and 15.