Respuesta :
The true statements about the graph y = 4x2 + 28x + 49 are as follows;
(b) The equation 2x + 7 = 0 can be used to find a zero of the function.
(d) The graph has a double root at x = -7/2.
(e) The graph intersects the y-axis at y = 49.
What is the function of the graph?
The graph of a function f is the graph of the equation y = f (x).
The function is given as:
[tex]\rm y = 4x^2 + 28x + 49[/tex]
Express 28x and 14x + 14x; so, we have:
[tex]\rm y = 4x^2 + 14x+14x + 49[/tex]
Factorize
[tex]\rm y = 4x^2 + 14x+14x + 49\\\\y = 2x(2x+7)+7(2x+7)\\\\y=(2x+7)(2x+7)[/tex]
Express as a perfect square
[tex]\rm y = (2x+7)^2[/tex]
This means that the graph of the equation has a double root.
It also means that 2x + 7 = 0 can be used to determine the root/zero of the function.
Substitute 0 for x in to determine the y-intercept
[tex]\rm y = (2x+7)^2\\\\\rm y = (2(0)+7)^2\\\\\rm y = (0+7)^2\\\\y=49[/tex]
This means that the graph intersects with the y-axis at y = 49
Hence, the true statements are (b), (d), and (e)
Read more about quadratic functions at:
brainly.com/question/11441586
