The equation of parabola is y = 3x²- 12x+ 15.
<u>Step-by-step explanation:</u>
The equation of the parabola is given as y = x².
If it has a vertex then the equation can be written as,
y = a(x-h)² + k
where (h, k ) is the vertex and a is the stretching or compressing factor.
So here the vertex is (2,3) and it is vertically stretched by 3.
So the equation is given as,
y = 3(x-2)² + 3
y = 3(x² -4x+4) + 3
= 3x² - 12x + 12 + 3
y = 3x²- 12x+ 15 is the equation of the parabola.
Answer:
slope = 2
Step-by-step explanation:
Find 2 points on the line that land perfectly on the grid. I'll choose these 2 here:
(-2, -1) and (0, 3)
Rise is the change in the y value from one point to the other, and run is the change in the x. Looking at these 2 points, y went from -1 to 3. That is a <em>rise</em> of 4. The x went from -2 to 0, so that is a <em>run</em> of 2. "rise over run" means rise literally over run in a fraction like this:

The more proper way to calculate slope looks like this, but it's really the same thing in the end:

where (x1, y1) and (x2, y2) are your 2 points.
Finally, the slope of this line is:

That's a rise of 4 over a run of 2, and that simplifies to just a slope of 2.
Answer: 
Step-by-step explanation:
The equation of the line is Slope-intercept form is:

Where "m" is the slope and "b" the y-intercept.
The slopes of perpendicular lines are negative reciprocal.
Then, if the slope of the first line is -3, the slope of the other line must be:

Substitute the point (3,4) into the equation and solve for b:

Then the equation of this line is:

Answer:

Step-by-step explanation: