Question

based on the graph, circle the ordered pair that is a solution to the equation:

1. (-1, 2)

(1, -1)
(0, .3)

1. (0, -6.2)

(-0.61, 0)
(0.5, 1.3)

identify true or false

1. the equation: $f(x)=-(x + 3)^2 + 4$ is reperested on the graph below.

the line of symmetry of $f(x)$ is $x=2$ true or false
the maximum of the graph is at (-3, 4) true or false
the domain of the graph is all real numbers true or false
the x-intercepts are: (-5,0) and (-1, 0) true or false

circle the approximate solutions to $f(x)=g(x)$
34)
$x = -1$ $x = 1.3$ $x = 0$ $x = 2.3$ $x = 3.1$
35)
$x = -2.3$ $x=0$ $x=1$
$x=-1.4$ $x=1.6$ $x =3.6$

Explanation:

Step1: Check 31) graph points

For the first parabola, verify each ordered pair:

• $(-1,2)$: The graph at $x=-1$ has $y>3$, not 2.
• $(1,-1)$: The graph at $x=1$ has $y<-2$, not -1.
• $(0, 0.3)$: The graph at $x=0$ has $y\approx0.3$, which matches.

Step2: Check 32) graph points

For the second parabola, verify each ordered pair:

• $(0,-6.2)$: The graph at $x=0$ has $y=3$, not -6.2.
• $(-0.61,0)$: The graph crosses the x-axis near $x\approx-0.61$, which matches.
• $(0.5,1.3)$: The graph at $x=0.5$ has $y<0$, not 1.3.

Step3: Analyze 33) parabola properties

Given $f(x)=-(x+3)^2+4$, vertex form is $f(x)=a(x-h)^2+k$:

1. Line of symmetry: $x=h=-3$, so $x=2$ is FALSE.
2. Maximum at $(h,k)=(-3,4)$, so this is TRUE.
3. Domain of all parabolas is all real numbers, so this is TRUE.
4. Find x-intercepts: set $-(x+3)^2+4=0$

$$(x+3)^2=4 \implies x+3=\pm2 \implies x=-5 \text{ or } x=-1$$
So intercepts $(-5,0),(-1,0)$ are TRUE.

Step4: Find 34) intersection points

For $f(x)=g(x)$, find x-values where graphs cross:

• Graphs cross at $x=-1$ and $x=3.1$.

Step5: Find 35) intersection points

For $f(x)=g(x)$, find x-values where graphs cross:

• Graphs cross at $x=-2.3$ and $x=1.6$.

Answer:

1. $\boldsymbol{(0, .3)}$
2. $\boldsymbol{(-0.61, 0)}$

33)

• The line of symmetry of $f(x)$ is $x=2$: $\boldsymbol{FALSE}$
• The maximum of the graph is at $(-3, 4)$: $\boldsymbol{TRUE}$
• The domain of the graph is All Real Numbers: $\boldsymbol{TRUE}$
• The x-intercepts are: $(-5,0)$ and $(-1, 0)$: $\boldsymbol{TRUE}$

1. $\boldsymbol{x=-1}$, $\boldsymbol{x=3.1}$
2. $\boldsymbol{x=-2.3}$, $\boldsymbol{x=1.6}$