Question

Given the quadratic function f(x) = -x? - 7x+3, address the following. a. Does the function have a maximum or minimum value? b. What is this maximum or minimum value? a. Does the function have a maximum or minimum value? O Minimum O Maximum

Answer 1

f() = x2 – 7x+3

here coefficient of x² is negative so function has maximum value

.

.

f() = x2 – 7x+3

f (x) = + (22 +212) +3

middle term is 21 to convert into vertex form we need to add and subtract $\left ( \frac{21}{2} \right )^2$

- (n) =+(2+218 + () +- (*)") +

(a) = - (7+ 4) - (1) ) + 4

11༠) - (༢༣ –) - 4༠) ༧

Y(0) - (+4) - (-1) 4 , ༡

++ () - (1)

f (x) =} (+) +*+1

10. 21 2 147 + 12

.+ (+)-

.

compare with vertex form of parabola

y = a(- h)2+k

so here vertex is

(15, 6) = (1)

and maximum value is

159