**you**to at least try these yourself. Do you not know what "completing the square" means?

Also, if you do not want to use latex, at least use "^" to indicate powers.

Show an effort and we will make suggestions.Sarii said:

1. Convert the following functions into the vertex form of the quadratic equation by completing the square. Show each step clearly.

a. y = x2 + 6x + 20

Answer:

b. y = x2 - x +

Answer:

c. y = - 4x2 + 24x + 14

Answer:Click to expand

Once you have "completed the square", you will have something of the form y= -a(x- b)^2+ c. Since a square is never positive, -a(x- b)^2 is never positive: y is c2. Annette takes a jump on a snowmobile and lands on a level snowfield several metres from her takeoff point. Her path through the air could be described using the function y = - x2 + x, where y is measured in metres.

a. Clearly show how to convert the function y = - x2 + x into the vertex form of the quadratic equation by completing the square.

Answer:

b. How high will Annette and the snowmobile rise in the jump?Click to expand

**minus**something and so its largest value is c.

The y- level at the takeoff point is y= 0. Annette will land when y= 0 again. Solve the equation x^2+ x= 0. x= 0 is an obvious answer- that is the takeoffpoint. The other solution is the x value of the landing point.Answer:

c. How far from the takeoff point will Annette land? Explain how you arrived at that answer.

Answer:Click to expand

Sours: https://mathforums.com/threads/a-y-xx/

## Given the equation y = 2x^2 + 6x - 20, find the slope of the curve at the point (4, 36) and the

### Question:

Given the equation {eq}y = 2x^2 + 6x - 20 {/eq}, find the slope of the curve at the point {eq}(4, \; 36) {/eq} and the equation(s) of the tangent line at the same point.

### Slope of a Curve at a Point:

1) A tangent line is a limiting position of a secant line to a curve.

2) {eq}f{}'\left ( a \right ) {/eq} is the slope of the tangent line to the curve {eq}y=f\left ( x \right ) {/eq} at {eq}x = a {/eq}.

3) Point-Slope Form of a Line: The equation of a line passing through a point {eq}\left ( x_{0},y_{0} \right ) {/eq} having slope {eq}m {/eq} is {eq}y=y_{0}+m\left ( x-x_{0} \right ) {/eq}

### Answer and Explanation: 1

We start by finding the first derivative of the given function:

{eq}\begin{align*} y&=2x^2+6x \\ \Rightarrow \frac{\mathrm{d} y}{\mathrm{d}

See full answer below.

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## Properties of a straight line

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(6*x)=0

### Step 1 :

#### Equation of a Straight Line

Solve y-6x+20 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"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 y-6x+20 = 0 and calculate its properties

#### Graph of a Straight Line :

#### Calculate the Y-Intercept :

Notice that when x = 0 the value of y is /1 so this line "cuts" the y axis at y=

y-intercept = /1 =#### Calculate the X-Intercept :

When y = 0 the value of x is 10/3 Our line therefore "cuts" the x axis at x=

x-intercept = 20/6 = 10/3 =#### Calculate the Slope :

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 and for x=, the value of y is So, for a change of in x (The change in x is sometimes referred to as "RUN") we get a change of - () = in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = / =### Geometric figure: Straight Line

- Slope = / =
- x-intercept = 20/6 = 10/3 =
- y-intercept = /1 =

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## 20 y=6x

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**99**100 101