Question

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

A. In vertex form, f(x) = 2(x - 2)2 +1 and therefore has a minimum value of 1.
B. In vertex form, f(x) = 2(x - 2)2 + 1 and therefore has a minimum value of 2.
C. In vertex form, f(x) = 2(x - 2)2 + 4.5 and therefore has a minimum value of 4.5.
D. In vertex form, f(x) = 2(x - 2)2 + 4.5 and therefore has a minimum value of 2.
А
b
B
С
D

Answer 1

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

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.