ACT 1 Alg: Relate factors, solutions, zeros, and intercepts

Welcome to your ACT 1 Alg: Relate factors, solutions, zeros, and intercepts

$Q_{1}:$ The factored form of the function in graph below is

$(x-1)(x+3)$

$(x+1)(x-3)$

$(x+1)(x+3)$

$(x-1)(x-3)$

$Q_{2}:$ One of the following statement is Not true

On a graph, the solution of the function is the $x$-intercept(s)

Solutions of functions is called roots

Solutions of functions is called zeros

The solutions of a quadratic function are the values of $x$ for which $f(x)\neq 0$

$Q_{3}:$ The factored form of a quadratic function can be written in the form $f( x)= a(x- b)( x -c)$. The $x$-intercepts of the function is/are

$x=b$ only

$x=c$ only

$x=b,c$ only

$x=a$ only

$Q_{4}:$ Given $f(x)=(x-2)(x+1)$, then the solution of $f(x)$ is

$2,1$

$-2,1$

$-2,-1$

$2,-1$

$Q_{5}:$ Given $f(x)=-(x+2)(x-4)$, which of the following is one of $x$-intercepts

$x=-2$

$x=-4$

$x=0$

$x=6$

$Q_{6}:$ One of the following statement is Not true

the maximum number of real solution of quadratic is three

roots or zeros of the function is the same

the numbers of root in quadratic can be $4$

if there is no $x$-intercept, then the function have no solutions

$Q_{7}:$ The graph of the equation $g(x)=a(x-1)(x+5)$ is a parabola with vertex $(h,k)$. What is the solution of $g(x)$?

$1,-5$

$a$

$-5$

$1,-5,a$

$Q_{8}:$ The solution of equation $(2x-5)(3x-10)=0$ is

$x=\frac{-5}{2} , \frac{10}{3}$

$x=\frac{5}{2} , \frac{10}{3}$

$x=\frac{5}{2} , \frac{-10}{3}$

$x=\frac{-5}{2} , \frac{-10}{3}$

$Q_{9}:$ If $x+ y = 7$ and $x -y = 2$ , what is the value of $x^{2}-y^{2}$?

$40$

$20$

$14$

$36$

$Q_{10}:$ The factor of $ax^{2}+bx+c$ is

$(x+\frac{b\pm \sqrt{b^{2}-4ac}}{2a})$

$(x-\frac{b\pm \sqrt{b^{2}-4ac}}{2a})$

$(x-a)(x-b)$

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

$Q_{11}:$ If $s > 0$ and $4x^{2}-rx+9=(2x-s)^{2}$ for all values of $x $, what is the value of $r -s$ ?

$6$

$3$

$9$

$12$

$Q_{12}:$ In the quadratic equation $x^{2}-rx=\frac{k^{2}}{4}$, $k$ and $r$ are constants. What are the solutions for $x $?

$x=\frac{r\pm 2\sqrt{k^{2}+r^{2}}}{4}$

$x=\frac{r\pm \sqrt{k^{2}+r^{2}}}{2}$

x=\frac{2r\pm \sqrt{k^{2}+8r^{2}}}{4}

$x=\frac{r\pm \sqrt{k^{2}+2r^{2}}}{4}$

$Q_{13}:$ If $(x-7)(x-s)=x^{2}-rx+14$ for all values of $x$ , what is the value of $r+ s$?

$11$

$5$

$6$

$-10$

$Q_{14}:$ If $x^{2}-\frac{3}{2}x+c=(x-k)^{2}$, what is the value of $c $?

$\frac{16}{9}$

$16$

$\frac{9}{16}$

$9$

$Q_{15}:$ If $f(x)$ is a perfect-square trinomial, then the number of real root is?

$0$

$1$

$2$

$3$

$Q_{16}:$ On the graph $g(x)$ crosses the $x$- axis twice, then $g(x)$ having

$2$ factor and $2$ same root

$2$ factor and $2$ different root

$1$ factor and $1$ root

$1$ factor and $2$ same root

$Q_{17}:$ If discriminant of $k(x)$ is positive, then $k(x)$ having

one $x $- intercepts

no real roots

two $x $- intercepts

one real root

$Q_{18}:$ If $L(x)$ having no real root, then one of the following statement is false?

the discriminant is negative

there is no real solution

having factor $(x+r)(x+t)$ with $r,s\in R$

the graph of $L(x)$ does not cross the $x$- axis.

$Q_{19}:$ If $r_{1}$ and $r_{2}$ are roots of the quadratic equation $ax^{2}+bx+c=0$ , then $r_{1}+r_{2}=$

$-\frac{b}{a}$

$\frac{b}{a}$

$-\frac{c}{a}$

$\frac{c}{a}$

$Q_{20}:$ If $R(x)$ having root $2,4$, then the solutions of $R(x)$ is

$6,8$

$4,2$

$6,12$

no solution

$Q_{21}:$ Which of the following statement is true for table below?

having one $y$-intercept

having two $x$-intercepts

two real roots

all of them

$Q_{22}:$ Which of the statement is false for table below?

having one real solution

two $y$- intercepts

one $x$- intercepts

all of them

$Q_{23}:$ If $(ax+b)(2x-5)=12x^{2}+kx-10$ for all values of $x$ , what is the value of $k $?

$-26$

$24$

$32$

$-10$

$Q_{24}:$ If $B(x)=x^2-k$ where $K>0$, which of the following is true?

one real root only

two solution only

no $x$-intercept

none

$Q_{25}:$ Since the graph of $y = 2x ^{2} – 8x + 9$ does not cross the $x$-axis, the quadratic equation $2x ^{2} – 8x + 9 = 0$ has

has no real solutions

has two root

one $x$- intercept

none

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