找到你今天要练的题。

\( f(x)=x^2-20x+76 \) 
What is the minimum value of the given function?

\( f(x)=4x^2+56x+197 \) 
The function g is defined by \( g(x)=f(x+8) \). What is the minimum value of \( g(x) \)?

\( f(x)=4x^2+72x+325 \) 
The function g is defined by \( g(x)=f(x+6) \). What is the minimum value of \( g(x) \)?

\( f(x)=2x^2+28x+99 \) 
The function g is defined by \( g(x)=f(x+6) \). What is the minimum value of \( g(x) \)?

\( f(x)=(x-6)(x+11) \) 
The function \( f \) is defined by the given equation. For what value of x does \( f(x) \) reach its minimum?

Function \( f \) is a quadratic function. The graph of \( y=f\left(x\right) \) in the xy-plane has a vertex at \( \left(4,-6\right) \), contains the point \( \left(3,-8\right) \), and has a y-intercept at \( \left(0,\ a\right) \) . The graph of  \( y=5\ ·\ f\left(x\right) \) has a y-intercept at \( \left(0,\ b\right) \). What is the positive difference between a and b?

\( f\left(x\right)=5x^2+90x+406 \) 
The function g is defined by \( g\left(x\right)=f\left(x+8\right) \) . What is the minimum value of g(x)?

The graph of the equation \( y=5(x-n)^2 \), where n is an integer constant, is shown. What is the value of n?

\( f(x)=2x^2-17x+33 \) 
The given equation defines the function \( f \). For what value of x  does \( f(x) \) reach its minimum?

\( y=x^2-14x+22 \) 
The given equation relates the variables x and y. For what value of x does the value of y reach its minimum?

A physics class is planning an experiment about a toy rocket. The equation \( y=-16\left(x-5.6\right)^2+502 \) gives the estimated height y, in feet, of the toy rocket x seconds after it is launched into the air. Which of the following is the best interpretation of the vertex of the graph of the equation in the xy-plane?

f(x)= 4x² - 50x + 126 The given equation defines the function f. For what value of x does f(x) reach its minimum?