Jeffrey Is Asked To Graph F(X)=X^2-6x+5. Below Is His Graph. Is His Graph Correct Or Incorrect?, Prove Your Answer By Discussing The Key Characteristi

Jeffrey is asked to graph f(x)=x^2-6x+5. Below is his graph. Is his graph correct or incorrect?

Prove your answer by discussing the key characteristics of a quadratic function. Include the shape of the graph based on its leading coefficient, calculation of its vertex, maximum or minimum value as well as its x -intercepts.

 

Answer with Step-by-step explanation:

Quadratic function:

f(x) = x² - 6x + 5

a = 1  (the leading coefficient)  ⇒  a > 0  graph opens upward

b = -6

c = 5

Find the vertex (h, k) where h=axis of symmetry and k = maximum or minimum value depending on value of a:

h = -b/2a

h = -(-6)/(2)(1)

h = 6/2

h = 2

k = f(h) = (h)²- 6h + 5

k = (2)² - 6(2)+5

k = 4 -12 + 5

k = -3

Vertex (h,k): (2, -3)

h = axis of symmetry = 2

Since a > 0, the parabola (graph) of the function opens upward, and has a minimum value (k) = - 3.

Find the x-intercepts or roots/zeros of the function by factoring:

x² - 6x + 5 = 0

(x - 5) (x - 1) = 0

x - 5 = 0

x = 5

x - 1 = 0

x = 1

x = {5, 1}

The x-intercepts are 5 and 1.

Therefore, Jeffreys graph is incorrect because it has x-intercepts 2 and 6.

The vertex is (4, -4)

The axis of symmetry is 4.

The minimum value is -4.