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.
