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djverab [1.8K]
3 years ago
11

(Algebra II) Standard Form of a Quadratic Function - I'm having trouble with two questions on this quiz? Please don't just give

answers, try to explain so I can understand.
1). What are the vertex and the axis of symmetry of the equation? y = –2 x 2 + 8 x – 18

5). The graph below models the acceleration of a car. Interpret the meaning of the vertex.

Mathematics
2 answers:
anastassius [24]3 years ago
6 0
1.
the x value of the vertex in form
ax^2+bx+c=y
is
-b/2a
so

-2x^2+8x-18
x value of vertex is
-8/(2*-2)=-8/-4=2

plug it in to get y value
-2(2)^2+8(2)-18
-2(4)+16-18
-8-2
-10

vertex is at (2,-10)
or you could complete the square to get into y=a(x-h)^2+k, where the vertex is (h,k)
so as follows
y=(-2x^2+8x)-18
y=-2(x^2-4x)-18
y=-2(x^2-4x+4-4)-18
y=-2((x-2)^2-4)-18
y=-2(x-2)^2+8-18
y=-2(x-2)^2-10
vertex is (2,-10)






5.
vertex is the time where the speed is the highest
at about t=10, the speed is at its max
Amanda [17]3 years ago
5 0
The vertex of the graph is the point where the line crosses its axis of symmetry.
The axis of symmetry is the line that you could fold the graph on and it would be symmetrical about that line. 
In your graph you could fold it on the x=10 line (which is a vertical line (goes up and down)) and the graph would be symmetrical. This is saying that you could technically fold this graph in HALF and it would be 100% symmetrical if you were to fold it on that line.
Therefore your vertex is the point on the graph where your line crosses the axis of symmetry which would be (10,something). 
Looking at your graph it is (10,60).
Let me know is you need me to explain further
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Graph: y &lt; 1/3x+1/2<br> graph the point
Galina-37 [17]

Answer:

1/11

Step-by-step explanation:

First you have to times 1/3 and 1/2 and then you get 1/6. Then you add 1/3 and 1/2 and that's 1/5. then you add them both.

5 0
3 years ago
Solve the inequality. 4x+6&lt;3x-5 A)x&lt;1 B) x&lt;11 C) x&lt;-1 D)x&lt;-11
klasskru [66]

4x + 6 < 3x - 5 is our given inequality

4x < 3x -11 by subtracting 6 on both sides of the inequality sign

x < -11 by subtracting 3x on both sides.


Thus, x < -11 -- choice D -- is the solution.

4 0
3 years ago
Let f(x)=(8x^4-3)^3 and g(x)=8x^4-3 given that f(x)=(h g)(x) , find h(x)
Harman [31]

<u>Answer:</u>

h(x) = x^{3}

<u>Step-by-step explanation:</u>

f(x) = (8 \times x^{4}- 3)^{3} ------------(1) (given)

g(x) =(8 \times x^{4}- 3) -------------(2) (given)

so,

f(x) = h(g(x)) (given)

    = (g(x))^{3}-----(from (1) and (2))

⇒h(k) = k^{3}-----(taking g(x) = k)

⇒h(x) = x^{3} is the function.

8 0
3 years ago
You have 8 cups of flour. A recipe calls for 2/3cup of flour. Another recipe calls for 1/4 cup of flour. How much flour do you h
Sonja [21]
There will be 5 more because 8-2-1 =5
6 0
3 years ago
What is the equation of this graphed line?
barxatty [35]

Answer:

y=-\frac{1}{3}x-5

Step-by-step explanation:

Given:

The two points on the line are:

(x_1,y_1)=(-6,-3)\\(x_2,y_2)=(6,-7)

Now, for a line with two points on it, the slope of the line is given as:

m=\frac{y_2-y_1}{x_2-x_1}

For the points (x_1,y_1)=(-6,-3)\ and\ (x_2,y_2)=(6,-7), slope is:

m=\frac{-7-(-3)}{6-(-6)}\\m=\frac{-7+3}{6+6}\\m=\frac{-4}{12}=-\frac{1}{3}

Now, for a line with slope 'm' and a point (x_1,y_1) on it is given as:

y-y_1=m(x-x_1)

Plug in all the values and determine the equation of the line. This gives,

y-(-3)=-\frac{1}{3}(x-(-6))\\\\y+3=-\frac{1}{3}(x+6)\\\\y+3=-\frac{1}{3}x-\frac{1}{3}\times 6\\\\y+3=-\frac{1}{3}x-2\\\\y=-\frac{1}{3}x-2-3\\\\y=-\frac{1}{3}x-5

Therefore, the equation of the line is:

y=-\frac{1}{3}x-5

4 0
3 years ago
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