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
To answer, allow the width of the frame to be represented by x. The dimensions of the frame should then be, 11+2x and 6+2x. Subtracting the area of the inside of the frame from the area of the outside should be able to give us 18 cm². The equation,
(11 + 2x)(6 + 2x) - (11)(6) = 18
The value of x from the equation is equal to 0.5. Thus, the width of the frame should be 0.5 cm.
Answer:
80
Step-by-step explanation:
180-(60+40)=180-60-40=180-100=80
Answer:
who know maybe there is none
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