數學題目一題(f.4) ((急))

y = ax² + bx + 1
(a). Find the values of a and b
5 = a(2)² + b(2) + 1
5 = 4a + 2b + 1
2a + b = 2 --------- (1)
11 = a(-1)² + b(-1) + 1
11 = a - b + 1
a - b = 10 ----------- (2)
(1) + (2), 3a = 12
a = 4
4 - b = 10
b = -6

(b) Find the maximum or minimum value of y and the corresponding value of x
y = 4x² - 6x + 1
= 4(x² - 3x/2) + 1
= 4(x² - 3x/2 + 9/16) - 9/4 + 1
= 4(x - 3/4)² - 9/4 + 1
= 4(x - 3/4)² - 5/4
minimum value = -5/4
corresponding value of x = 3/4

(c) Write down the vertex and the axis of symmetry of the graph of the function
vertex : (3/4, -5/4)
and the axis of symmetry : x = 3/4

(a)
5=a(2)²+b(2)+1
2a+b=2----(1)
11=a(-1)²+b(-1)+1
a-b=10----(2)
(1)+(2)
3a=12
a=4
in (2)
4-b=10
b=-6
(b)
y=4x²-6x+1
=4(x²-3x/2)+1
=4(x-3/4)²-5/4
the minimum=-5/4
(c)the vertex(3/4,-5/4)