Question

If f(x) = 2x2 – 8x + 9, which statement regarding the vertex form of f(x) is true?

Answer 1

Answer:

A. In vertex form, f(x) = 2(x - 2)² +1 and therefore has a minimum value of 1.

Step-by-step explanation:

Function is given as;

f(x) = 2x² - 8x + 9

From quadratic formula, we know that;

a = 2

b = -8

c = 9

Now, x-coordinate of the vertex is;

x = -b/2a

x = -(-8)/2(2)

x = 2

Let's find the y-coordinate;

f(2) = 2(2)² - 8(2) + 9

f(2) = 8 - 16 + 9

f(2) = 1

Thus, y-coordinate = 1

This means the vertex coordinate is (2, 1)

Now, vertex form of a quadratic equation is;

f(x) = a(x - h)² + k

Where, (h, k) is the coordinate of the vertex and a is the first term as earlier seen.

Thus;

f(x) = 2(x - 2)² + 1

Now, the leading coefficient is positive and so it means that the parabola will open upwards and thus, will have a minimum value of 1.