Question

Please help me with this graph.

Answer 1

• f(x) = 1/4(x + 4)(x - 2)²

Explanation:

Let's analyze the graph.

We observe that:

• It is an increasing function, so leading coefficient is positive,
• It has one x-intercept (- 4, 0),
• It has one touching point at x-axis (2, 0), so it has at least multiplicity of 2,
• It has a y-intercept (0, 4),
• It has a local maximum (- 2, 8).

Based on our observations, the least degree polynomial function will have the form of:

• f(x) = a(x + 4)(x - 2)²

To find the value of a we'll use the y-intercept:

• 4 = a(0 + 4)(0 - 2)²
• 4 = a*16
• a = 4/16
• a = 1/4

Let's prove it with local maximum:

• 8 = 1/4(- 2 + 4)(-2 - 2)²
• 8 = 1/4*2*16
• 8 = 8

So the function is:

• f(x) = 1/4(x + 4)(x - 2)²