Function f is represented by the equation shown.

f(x)=x^2-4x+3

function g has a vertex at (1,3) and the parabola opens downwards.
which statement is true?

a.
the y-intercept of function f is greater than the y-intercept of function g.
b.
the y-intercept of function f is less than the y-intercept of function g.
c.
the minimum of function f is at (-4,3).
d.
the minimum of function g is at (1,3).

Step-by-step explanation:

A. y-Intercept of ƒ(x)

ƒ(x) = x² - 4x + 3

f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3

The y-intercept of ƒ(x) is (0, 3).

If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).

Statement A is TRUE.

B. y-Intercept of g(x)

Statement B is FALSE.

C. Minimum of ƒ(x)

ƒ(x) = x² - 4x + 3

a = 1; b = -4; c = 3

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

h = -b/2a = -(-4)/(2×1 = 2

k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1

The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).

Statement C is FALSE.

D. Minimum of g(x)

g(x) is a downward-opening parabola. It has no minimum.

Statement D is FALSE

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

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