Respuesta :
Answer:
[tex]y=2x^2+8x+8[/tex]
Step-by-step explanation:
Notice that we are looking for a quadratic function that has only one real solution for y=0, that is a unique point that touches the x-axis
We need therefore to look at the discriminant associated with all 4 equations constructed by equaling y to zero. We then try to find one that gives discriminant zero , corresponding to a unique real solution to the equation.
a) [tex]9x^2+6x+4=0[/tex] has discriminant: [tex]6^2-4(9)(4)=-108[/tex]
b) [tex]6x^2-12x-6=0[/tex] has discriminant: [tex](-12)^2-4(6)(-6)=288[/tex]
c) [tex]3x^2+7x+5=0[/tex] has discriminant: [tex](7)^2-4(3)(5)=-11[/tex]
d) [tex]2x^2+8x+8=0[/tex] has discriminant: [tex](8)^2-4(2)(8)=0[/tex]
Therefore, the last function is the one that can have such graph