3.1 Quadratic functions (in class)

Let [math]f(x)=3(x+2)^2-6[/math] be a quadratic function. If [math]f(6)=m[/math], which of the following numbers is also [math]m[/math]?

Let [math]f(x)=a(x+5)(x-1)[/math] where [math]a[/math] is a negative number. If the range of [math]f(x)[/math] is [math](-\infty,18][/math], what is the value of [math]a[/math]?

Let [math]f(x)=a(x-h)^2+k[/math] be a quadratic function where [math]a, h[/math] and [math]k[/math] are constants. If we translate [math]f(x)[/math] 4 units to the right and 3 units up, then the new function will be [math]y=3(x+4)^2+1[/math]. Find the values of [math]a, h[/math], and [math]k[/math].

Let [math]f(x)[/math] be a quadratic function. Suppose [math]f(x)[/math] passes through [math](1,-1), (-5,-1)[/math], and [math](-2,2)[/math]. Find the [math]y[/math]-intercept of [math]f(x)[/math].

To find the vertex form of [math]y=4x^2-4x-3[/math], we rewrite the function as [math]4(x^2-x)-3[/math], and then we add and subtract a constant [math]c[/math] in the parentheses to make a perfect square, what is the value of [math]c[/math]?

Consider a quadratic function [math]f(x)=-3x^4+6x^2-1[/math]. Find the maximum value of [math]f(x)[/math].

Let [math]f(x)=-x^2-x+3[/math] be a quadratic function with domain [math][1,4)[/math]. What is the range of [math]f(x)[/math]?

Let [math]f(x)[/math] be a quadratic function. Suppose [math]f(-5)=f(5)=4[/math]. Which value cannot be the [math]y[/math]-intercept?

What is the range of [math]f(x)=x^2+10x-2[/math] where [math]-10\leq x<-1[/math]?

What is the minimum of [math]f(x)=4x^2-12x+9[/math] where [math]x\leq2[/math]?

(Calculator) Consider a parabolic cup. We pour some water into the cup. When the depth of the water is 8cm, the diameter of the water surface is 6cm. Suppose we keep pouring water into the cup until the depth of the water reaches 10cm. If the diameter of the water surface is [math]a\sqrt{b}[/math] where [math]a[/math] and [math]b[/math] are prime numbers, what are [math]a[/math] and [math]b[/math]?