DSAT extra practice Ch3 Lv3

The figure above shows the graph of a quartic polynomial function [math]f(x)[/math]. If [math]g(x)=f(x)+k[/math] has two [math]x[/math]-intercepts, which of the following values could be [math]k[/math]?

If [math]a[/math] is a constant and [math]a\neq0[/math], which of the following polynomial functions \textbf{must have} [math]x[/math]-intercept?

$$x+2y=\sqrt{72}$$$$x-2y=\sqrt{8}$$If [math](x,y)=(a,b)[/math] is the solution to the equations system above, what is the value of [math]a^2-4b^2[/math]?

$$(x+y)^2-10(x+y)+25=0$$Which of the following could be a solution to the equation above?

If polynomial [math]f(x)[/math] has 10 [math]x[/math]-intercepts, which of the following numbers could not be the degree of [math]f(x)[/math]?

Let [math]f(x)[/math] be a polynomial having three factors [math]x-1, x-3[/math] and [math]x+4[/math]. If [math]g(x)=f(x+2)[/math], which of the following is the equation of [math]g(x)[/math]?

$$x^2+ax+12=0$$If the equation above has two integer solutions, which of the following numbers could not be [math]a[/math]?

$$x^4+x^2-12$$If [math]x+a[/math] is a factor of the polynomial above where [math]a[/math] is a constant, what is the value of [math]a^2[/math]?

The figure above shows the graph of quadratic function [math]f(x)=ax^2+bx+c[/math], which of the following statements about [math]b[/math] is true?

If a quadratic function [math]f(x)[/math] passes through [math](2,0)[/math] and the origin, which of the following equations could not be [math]f(x)[/math]?

Consider a quadratic function [math]f(x)=x^2-6x+8[/math] with domain [math][-1,1][/math]. What is the minimum value of [math]f(x)[/math]?

Let [math]f(x)[/math] be a quadratic function. If [math]f(1)=f(5)=7[/math], which of the following could be [math]f(x)[/math]?

$$f(x)=-3x^2+6$$Which of the following functions whose axis of symmetry is different from [math]f(x)[/math]?

$$x^2+8x-7=0$$If [math]x=a+\sqrt{b}[/math] is a solution to the equation above where [math]a[/math] and [math]b[/math] are constants, what is the value of [math]a+b[/math]?

$$x^2+bx+c=0$$If [math]x=6\pm\sqrt{12}[/math] are the solutions to the equation above, what is the value of [math]b[/math]?

$$x^2-5x+k=0$$If the equation above has only one real solution, what is the value of [math]k[/math]?

$$f(x)=-3x^2+bx-75$$If the range of [math]f(x)[/math] is [math](-\infty,0][/math], what is the value of [math]b[/math]?

If [math]f(x)=ax^2+2x-6[/math] and [math]g(x)=3x+1[/math] has two intersections where [math]a[/math] is a negative integer, how many possible values of [math]a[/math]?

If the minimum value of [math]f(x)=ax^2+bx+c[/math] is 8, which of the following statements could be false?

$$f(x)=x^2+6x+3$$If [math]f(x)[/math] touches the line [math]\ell: y=2x+k[/math] at [math](a,b)[/math] where [math]a, b[/math], and [math]k[/math] are constants, what is the value of [math]a[/math]?

A soft cheese stick 15 feet long is cut into two parts, one part being [math]x[/math] feet long. If we place them around two pizzas with different size, which of the following expressions best represent the summation of the areas of these two pizzas?

Luna wants to plant 50 apple trees in her garden. Every apple tree can produce 80 apples. Since the nutrient of her garden is fixed, for every apple tree reduced, the number of apples a tree produces increases by 3. How many apple trees should Luna plant to maximize the number of apples?