DSAT extra practice Ch3 Lv1

$$x^5+x^3+x^3+x^2+x^2+x^2+1$$How many terms does the polynomial have?

$$f(x)=2x^3-x^2+3x+4$$$$g(x)=6x^2-x+12$$In the polynomials above, what is the constant term of [math]3f(x)-4g(x)[/math]?

$$(2x^4+3x^3-4x^2+1)(3x^3+5x-7)$$What is the degree of the polynomial above?

$$(x-3y)^2$$Which of the following expressions is equivalent to the expression above?

If [math]ab=5[/math], what is the value of [math](a+b)^2-(a-b)^2[/math]?

If [math]p^2+2pq+q^2=14[/math], what is the value of [math]p+q[/math]?

$$(p+q)^2-(p-q)^2=2048$$If [math]p=128[/math], what is the value of [math]q[/math]?

$$(2x^2+3y)^2$$What is the coefficient of [math]x^2y[/math] term of the polynomial above?

If [math]p^2+q^2=-2pq[/math] where [math]p[/math] and [math]q[/math] are constants, which of the following must be true?

$$f(x)=(2x+1)(3x+1)(4x+1)$$If [math]g(x)=f(x)+2[/math], which of the following values is not equal to 2?

The figure above shows the graph of polynomial function [math]f(x)[/math]. Which of the following is not a factor of [math]f(x)[/math]?

Let [math]f(x)[/math] be a polynomial function. If the graph of [math]f(x)[/math] passes through the origin, which of the following could not be [math]f(x)[/math]?

Let [math]f(x)[/math] be a polynomial function. If [math]5x-2[/math] is a factor of [math]f(x)[/math], which of the following points is on the graph of [math]f(x)[/math]?

The figure above shows the graph of polynomial function [math]f(x)[/math]. Which of the following equations is [math]f(x)[/math]?

$$3x^2+x-2$$Which of the following is a factor of the polynomial above?

$$f(x)=(x^3+x)(x^2+4x+3)$$How many [math]x[/math]-intercepts does [math]f(x)[/math] have?

$$x^2+19x+a$$If the expression above can be written as [math](x+p)(x+q)[/math] where [math]p[/math] and [math]q[/math] are constants. What is the value of [math]p+q[/math]?

$$x^2+bx+25$$If the expression above can be written as [math](x+p)^2[/math] where [math]p[/math] is a positive integer, what is the value of [math]b[/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]c[/math] must be true?

(I have a graph)The figure above shows the graph of [math]f(x)[/math]. Which of the following equations could be [math]f(x)[/math]?

Let [math]f(x)=ax^2+c[/math] be a quadratic function where [math]a[/math] and [math]c[/math] are constants. Which of the following graphs could be [math]f(x)[/math]?

The figure above shows the graph of quadratic function [math]f(x)=ax^2+bx+c[/math], what is the value of [math]\dfrac{b}{a}[/math]?

The figure above shows the graph of quadratic function [math]f(x)[/math]. What is the equation of the axis of symmetry?

$$f(x)=2(x-3)^2-5$$What is the range of the function above?

$$f(x)=a(x-h)^2+k$$If the maximum value of [math]f(x)[/math] is [math]-12[/math], which of the following is true?

Let [math]f(x)[/math] be a quadratic function. If [math]f(5)=f(-3)[/math] and the equation of the axis of symmetry is [math]x=k[/math], what is the value of [math]k[/math]?

$$f(x)=-(x+13)^2+19$$If [math]f(x)[/math] can be written as [math]-(x-p)(x-q)[/math] where [math]p[/math] and [math]q[/math] are constants, what is the value of [math]p+q[/math]?

$$f(x)=3(x+7)(x+5)$$What is the minimum value of [math]f(x)[/math]?

What is the summation of the solutions to the quadratic equation [math]x^2-8x-20=0[/math]?

Which of the following quadratic equations whose solutions are [math]5[/math] and [math]-3[/math]?

$$x^2=3x$$How many solutions does the equation have?

Which of the following is a solution to the equation [math]x^2+px+1=0[/math] where [math]p[/math] is a constant and [math]p>2[/math]?

$$x^2-7x+k=0$$In the equation above, [math]k[/math] is an integer. If the equation has no real solutions, what is the minimum of [math]k[/math]?

$$ax^2+9x+c=0$$If the equation above has only one real solution, what is the value of [math]ac[/math]?

The figure above shows the graph of quadratic function [math]f(x)=ax^2+bx+c[/math] where [math]a, b[/math] and [math]c[/math] are constants. Which of the following values must be positive?

$$f(x)=x^2+bx+c$$If the function above can be written as [math]f(x)=(x+p)^2[/math] where [math]p[/math] is a constant, which of the following is true?

Mia wants to understand the IQ of her pet dog, Molly, because she found that it usually does silly things. After conducting research, Mia uses a function $$f(x)=-0.5(x-7)^2+60$$to gauge Molly’s IQ, where [math]x[/math] represents Molly’s age, in months. In Molly’s life, what is her maximum IQ?

A jumping spider jumps from a table to the floor. Let$$f(t)=-0.4(t+2)(t-5)$$represent the relationship between time [math]t[/math], in seconds, and height, in inches. What is the height, in inches, of the table?

A pitcher throws a forkball, and the batter hits a homerun. The track of the baseball can be represented with the function $$h(x)=-\dfrac{1}{20}(x-20)^2+20$$where [math]x[/math] is the horizontal distance, in meters, between the baseball and the batter, and [math]h(x)[/math] is the height of the ball, in meters, above the ground. If the distance between the homerun wall and the batter is 36 meters, what is the maximum height of the homerun wall? Assume that the height of the wall is an integer.

$$f(t)=0.02t^2-0.8t+18$$The function above represents the relationship between time, in days, and the value of a stock in USD. Based on the function, when should we buy the stock? In other words, when is the value of the stock at its minimum?

Mia throws a can toward a trashcan. Let [math]f(t)[/math] be the function representing the height, in inches, of the can after [math]t[/math] seconds. If the highest height of the can is 8 inches when [math]t=3[/math], which of the following function could be [math]f(t)[/math]?