Answer:
2nd option
Step-by-step explanation:
given a quadratic in standard form
y = ax² + bx + c
• If a > 0 then minimum vertex
• If a < 0 then maximum vertex
Here a = - 1 < 0 then maximum
The maximum value is the value of the y- coordinate of the vertex
The x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
Here a = - 1 and b = 3 , then
x = - [tex]\frac{3}{-2}[/tex] = [tex]\frac{3}{2}[/tex]
Substitute this value into the equation for corresponding y- value
y = - ([tex]\frac{3}{2}[/tex] )² + 3([tex]\frac{3}{2}[/tex] ) - 1 = - [tex]\frac{9}{4}[/tex] + [tex]\frac{9}{2}[/tex] - 1 = - [tex]\frac{9}{4}[/tex] + [tex]\frac{18}{4}[/tex] - [tex]\frac{4}{4}[/tex] = [tex]\frac{5}{4}[/tex]
Then maximum value of [tex]\frac{5}{4}[/tex]
