Write the quadratic function in vertex form. y=-3x^2+24x-50
1 answer:
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Answer:
- Slope:
- x - intercept:
.
- y intercept:
.
Step-by-step explanation:
<u>Simplify:</u>
- Simplify the equation by subtracting what is to the right of the equal sign from both sides of the equation:
- 10*x+2*y-(20)=0.
<u>Step 1:</u>
- Pull out like factors:
- 10x + 2y - 20 = 2 * (5x + y - 10)
<u>Step 2:</u>
- Equations which are never true:
- Solve:
- 2 = 0
- This can't be solved.
- A non-zero constant never equals 0.
- Equation of a straight line:
- Solve: 5x+y-10 = 0
- "y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
- In this formula:
- y tells us how far up the line goes
- x tells us how far along
- m is the Slope or Gradient i.e. how steep the line is
- b is the Y-intercept i.e. where the line crosses the Y axis
- The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 5x+y-10 = 0 and calculate its properties
- Calculate the y-intercept:
- Notice that when x = 0 the value of y is 10/1 so this line "cuts" the y axis at y=10.00000
- y-intercept = 10/1 = 10.00000
- Calculate the x-intercept:
- Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 10.000 and for x=2.000, the value of y is -0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.000 - 10.000 = -10.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
- Slope = -10.000/2.000 = -5.000
<u>Answers:</u>
- Slope = -10.000/2.000 = -5.000
- x-intercept = 10/5 = 2
- y-intercept = 10/1 = 10.00000
