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
The original price was 7.
Chloe got a 15% discount; this means she paid 100-15 = 85% of the price. Letting x be the price, Chloe paid 0.85x.
Denise got a 20% discount; this means she paid 100-20 = 80% of the price. Denise paid 0.8x.
We know that Chloe paid 35p more; this gives us the equation
0.85x = 0.8x + 0.35
We do not want a variable on both sides, so we subtract 0.8x from both:
0.85x - 0.8x = 0.8x + 0.35 - 0.8x
0.05x = 0.35
Divide both sides by 0.05:
0.05x/0.05 = 0.35/0.05
x = 7
Answer:
3x-4y=-9
Step-by-step explanation:
