Respuesta :
Answer:
We have the following theorem:
If f is a quadratic function of the form [tex]f(x)=ax^2+bx+c[/tex] and [tex]ac<0[/tex], then the function f has two x-intercepts.
(a) [tex]g(x)=-8x^2+5x-2[/tex]
For this function a = -8 and c = -2, then [tex]-8\cdot -2=16[/tex] is greater than zero. Therefore, we cannot conclude anything.
(b) [tex]h(x) =-\frac{1}{3}x^2+3x[/tex]
For this function a = -8 and we don't know the value of c. Therefore, we cannot conclude anything.
(c) [tex]k (x) = 8x^2 - 5x - 7[/tex]
For this function a = 8 and c = -7, then [tex]8\cdot -7=-56[/tex] is less than zero. Therefore, we can conclude that the function k has two x-intercepts.
(d) [tex]j(x)=-\frac{71}{99} x^2+210[/tex]
For this function a = [tex]-\frac{71}{99}[/tex] and c = 210, then [tex]-\frac{71}{99}\cdot 210=-\frac{4970}{33}[/tex] is less than zero. Therefore, we can conclude that the function k has two x-intercepts.
(e) [tex]f(x)=4x^2-3x+7[/tex]
For this function a = 4 and c = 7, then [tex]4\cdot 7=28[/tex] is greater than zero. Therefore, we cannot conclude anything.
(f) [tex]F(x)=-x^4+x^3+9[/tex]
We cannot conclude anything because this is not a quadratic function.
