Determine if the quadratic function has a maximum or minimum value. Then find the value. The function is 4x^2 -28x+32

Question

Pls help i need this rn

Answer 1

4x² - 28x + 32

The leading coefficient of the quadratic is positive, so the parabola opens upwards.

If it opens upwards, it has a MINIMUM.

To find the vertex (h, k):

h = -b / (2a)

In this case:

a: 4

b: -28

c: 32

h = -(-28) / 2(4)

h = 28 / 8 = 3.5

h = 3.5

k = 4(3.5)² - 28(3.5) + 32

k = 49 - 98 + 32

k = -17

The quadratic has a MINIMUM at (3.5, -17)

Answer 2

f(x) = 4x² - 28x + 32 Downward opening parabola - maximum

f(x) = 4(x² - 7x + 8)

Maximum occurs at x = 7 / 2. What is it?