Which statements are true about the graph of the function f(x) = x2 - 8x + 5? Check all that apply.
The function in vertex form is f(x) = (x - 4)² - 11
The vertex of the function is (-8, 5)
The axis of symmetry is x = 5
The y-intercept of the function is (0, 5)
The function crosses the x-axis twice.

Solution:

Given f(x) = x² - 8x + 5

f(x) = x² - 8x + 16 - 16 + 5

f(x) = (x - 4)² - 16 + 5

f(x) = (x - 4)² - 11 --- (1)

This represents a parabola having the vertex at (4, -11) and the axis of this parabola is x = 4.

Statement (i) is true as observed from equation(1).

Statement (ii) is false as the vertex is at (4, -11).

Statement (iii) is false because the axis of symmetry is x = 4.

Statement (iv) is true because when x = 0 is substituted in f(x), we get f(x) = 5 = y. Thus the y intercept is (0, 5).

Statement (v) is true. Put f(x) = 0 in equation (1) then we get x = 4 + √11 and x = 4 - √11. Thus the curve cuts at (4 + √11, 0) and (4 - √11, 0).

Which statements are true about the graph of the function f(x) = x² - 8x + 5? Check all that apply.

Summary:

For the given function f(x) = x² - 8x + 5, the statements; “the function in vertex form is f(x) = (x - 4)² - 11” and " the y-intercept of the function is (0, 5) " and “the function crosses the x-axis twice” are true.