Question

Determine whether the

quadratic function
y=x² + 4x + 6 has
a maximum or minimum value.
Then find the value.
O maximum
minimum
The value is

Answer 1

(a) The function has a minimum value

(b) The minimum value is 2

Explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.

We know that for our function a = 1.

• When a > 0, the parabola opens upward and the vertex is a minimum
• When a < 0, the parabola opens downward and the vertex is a maximum

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1: First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2: Now we can plug in -2 for x in the quadratic function. The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.