the graph of which function will have a maximum and a y - intercept of 4?\n$f(x)=4x^{2}+6x…

the graph of which function will have a maximum and a y - intercept of 4?\n$f(x)=4x^{2}+6x - 1$\n$f(x)=-4x^{2}+8x + 5$\n$f(x)=-x^{2}+2x + 4$\n$f(x)=x^{2}+4x - 4$

the graph of which function will have a maximum and a y - intercept of 4?\n$f(x)=4x^{2}+6x - 1$\n$f(x)=-4x^{2}+8x + 5$\n$f(x)=-x^{2}+2x + 4$\n$f(x)=x^{2}+4x - 4$

Answer

Explanation:

Step1: Recall quadratic - function properties

For a quadratic function (y = ax^{2}+bx + c), if (a\lt0), the parabola opens downwards and has a maximum. The (y) - intercept is the value of the function when (x = 0), i.e., (y=c).

Step2: Check the sign of (a) and (y) - intercept for each function

  • For (f(x)=4x^{2}+6x - 1), (a = 4\gt0), the parabola opens upwards, no maximum.
  • For (f(x)=-4x^{2}+8x + 5), when (x = 0), (f(0)=5\neq4).
  • For (f(x)=-x^{2}+2x + 4), (a=-1\lt0), the parabola opens downwards (has a maximum), and when (x = 0), (f(0)=4).
  • For (f(x)=x^{2}+4x - 4), (a = 1\gt0), the parabola opens upwards, no maximum.

Answer:

(f(x)=-x^{2}+2x + 4)