ACT 1 Alg: Identify graphs of quadratic

Welcome to your ACT 1 Alg: Identify graphs of quadratic

$Q_{1}:$ If $f(x)=ax^{2}+bx+c$, then if $a>0$, the graph opens

upward

downward

leftward

rightward

$Q_{2}:$ If $f(x)=ax^{2}+bx+c$, then if $a<0$, the d the vertex is the

minimum point.

maximum point

both of them

none

$Q_{3}:$ If $f(x)=ax^{2}+bx+c$, then the equation of the axis of symmetry is

$x=\frac{-a}{2b}$

$x=\frac{b}{2a}$

$x=\frac{-b}{2a}$

none

$Q_{4}:$ If $f(x)=ax^{2}+bx+c$, then the vertex form of a quadratic function can be written in the form

$f(x)=a(x+h)^{2}+k$

$f(x)=a(x-h)^{2}+k$

$f(x)=a(x-h)^{2}-k$

none

$Q_{5}:$ On a graph, the solutions of a quadratic function is the

origin point

x-intercept(s)

y-intercept(s)

none

$Q_{6}:$ On a graph, to find the y-intercept of a parabola, the first step is ?

let $y=0$

let $x=0$

find x-intercept

none

$Q_{7}:$ If the parabola has two x-intercepts, then

the $x$-intercepts are equidistant from the axis of symmetry

the x-intercepts are not equidistant from the axis of symmetry

the x-intercepts are zero

none

$Q_{8}:$ Given $f(x)=x^{2}+2x-2$, then $y$ - intercept is

$-2$

$2$

$0$

there is no intercept

$Q_{9}:$ If $f(x)=x^{2}+16$, then the axis of symmetry is

$4$

$-16$

$1$

$0$

$Q_{10}:$ Given $f(x)=-(x+2)(x-4)$, then $x$ - intercept is

$-2$

$4$

$-2,4$

there is no intercept

$Q_{11}:$ Given $f(x)=-(x+2)(x-4)$, the coordinate of the vertex is?

$(1,9)$

$(1,7)$

$(2,4)$

$(-2,4)$

$Q_{12}:$ Which of the following is an equivalent form of the equation of the graph shown bellow, from which the coordinates of vertex $V$ can be identified as constants in the equation?

$y=(x-1)(x-5)$

$y=(x+1)(x+5)$

$y=x(x-6)+5$

$y=(x-3)^{2}-4$

$Q_{13}:$ Which of the following is an equivalent form of the equation of the graph shown above, that displays the $x$-intercepts of the parabola as constants?

$y=(x-1)(x-5)$

$y=(x+1)(x+5)$

$y=x(x-6)+5$

$y=(x-3)^{2}-4$

$Q_{14}:$ In the $xy$- plane above, the parabola $y= a(x- h)^{2}$ has one $x$-intercept at $(4,0)$ . If the $y$- intercept of the parabola is $9$, what is the value of $a $?

$\frac{9}{16}$

$\frac{16}{9}$

$9$

$16$

$Q_{15}:$ In the $xy$- plane, if the parabola with equation $ y=a(x+2)^{2}-15$ passes through $(1,3) $, what is the value of $a $?

$0$

$1$

$2$

$3$

$Q_{16}:$ The graph of the equation $y=a(x-1)(x+5)$ is a parabola with vertex $(h,k)$ . If the minimum value of $y$ is $−12 $, what is the value of $a $?

$\frac{-12}{9}$

$\frac{4}{3}$

$-12$

$-2$

$Q_{17}:$ The graph of the quadratic function above shows two $x$-intercepts and a $y$- intercept. Which of the following equations represents the graph of the quadratic function bellow?

$y=-\frac{(x-1)^{2}}{2}+9$

$y=-\frac{(x-2)^{2}}{2}+8$

$y=-\frac{(x-3)^{2}}{2}+8$

$y=-\frac{(x-2)^{2}}{2}+9$

$Q_{18}:$ In the figure below, the vertex of the graph of the quadratic function is at $(3,0) $. The points $B$ and $C$ lie on the parabola. If $ABCD$ is a rectangle with perimeter $38$, which of the following represents the equation of the parabola?

$y=\frac{2(x-3)^{2}}{5}$

$y=\frac{5(x-3)^{2}}{8}$

$y=\frac{3(x-3)^{2}}{4}$

$y=\frac{7(x-3)^{2}}{8}$

$Q_{19}:$ Which equation has the same graph as $2x^{2} − 4x − y + 11 = 0$?

$y=(2x-1)^{2}+9$

$y=(2x-1)^{2}+13$

$y=2(x-1)^{2}+9$

$y=2(x-1)^{2}+13$

$Q_{20}:$ A function $f(x)$ is graphed delow, which of the statement is true ?

the $x$-intercept is -3 only

have two same root

the $y$-intercept is 3 only

the sign of $x^{2}$ is positive

$Q_{21}:$ If the graph of $f(x)= 2x^{ 2} – 8x + 8 $ crosses the x-axis only at $2$, then $f(x)$

has only one real solution

has only two real solution

has no real solution

none

$Q_{22}:$ If $y = ax^{ 2}+ bx + c$ is the equation of a parabola whose axis of symmetry is?

a horizontal line

a vertical line

parallel to x-axis

line with slop 2

$Q_{23}:$ The vertex (turning point) of the parabola $y = 2x^{ 2} – 4x + 5$ is

$(-1,3)$

$(1,-3)$

$(3,1)$

$(1,3)$

$Q_{24}:$ For the equation of a parabola that passes through $(0, 4)$, $(1, 3)$, and $(2, 6)$, one of the following statement is not true.

the parabola opens upward

the parabola’s axis of symmetry is $x=-\frac{3}{4}$

the parabola’s $y$-intercept is 4

none

$Q_{25}:$ Which of the following is the equation of a parabola that does NOT intersect the $x$-axis?

$f(x)=x^{2}+4$

$g(x)=x^{2}-4x-4$

$h(x)=-x^{2}+1$

$k(x)=x^{2}$

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