Remember the shortcut way for graphing quadratic equations
- A quadratic function has graph as parabola
- Hence on both sides of vertex the parabola is symmetric and axis of symmetry is vertex x values .
- y on both sides for -x and +x is same
#1
Vertex
As a is positive parabola facing upwards
Find y for same x distance from vertex
I took 3-1=2 and 3+1=4
- f(2)=2(2-3)²-1=2(-1)²-1=2-1=1
- f(4)=2(4-3)²-1=1
Now plot vertex and these two points (2,1) and (4,1) on graph then draw a parabola by freehand
#2
- y=(x-2)(x+4)
- y=x²+4x-2x-8
- y=x²+2x-8
Convert to vertex form
Vertex at (-1,-9)
Same take two equidistant x values
Let's take -1-1=-2 and -1+1 =0
- f(-2)=(-2+1)²-9=1-9=-8
- f(0)=(1)²-9=-8
Put (-1,-9),(-2,-8),(0,-8) on graph and draw a freehand parabola
#3.
Yes it can be verified by finding the coordinate theoretically on putting them on function then can be verified through putting them on graph whether they matches or not
Answer:
x = 50
Step-by-step explanation:
Angles of a triangle add up to 180°. So the third angle of the triangle on the right is:
180° − 43° − 57° = 80°
Vertical angles are congruent, so the angle on the other side is also 80°. Therefore:
x° + x° + 80° = 180°
2x° = 100°
x = 50
73km. Hoped this helped!!
5k^3 - 3k + 7.-(-2k^3 + k^2 - 9)
7k^3 +k^2-3k +16
C. 7k^3 - k^2 - 3k + 16
Answer:
15% markup
Step-by-step explanation:
5% markup would be $1. Since 20*5% or 20*.05=1
We can multiply it by 3 to find the percent for $3 markup. Which is 15% or 0.15
