Exercise 1 Page 88

In order to identify whose throw travels higher, we need to determine the maximum height each throw traveled. We can utilize the equation for the axis of symmetry of a parabola to find the location of your throw. Quadratic Equation:& y= ax^2+ bx+ c Axis of Symmetry:& - b/2 a Now we need to substitute the values for the given equation into these formulas. Quadratic Equation:& y= - 16x^2+ 65x+ 5 Axis of Symmetry:& - 65/2( -16) This fraction can now be simplified.

-65/2(-16)

▼

Simplify

MultNegPos

(- a)b = - ab

-65/-32

DivNegNeg

- a/- b=a/b

65/32

Now we have identified the location of the axis of symmetry. This tells us the x-coordinate for your vertex. This means 6532 is the distance at which the maximum height of your throw occurs. We can substitute that value into the given equation to find the y-coordinate.

y=- 16x^2+65x+5

Substitute

65/32= x

y=- 16 ( 65/32 ) ^2+65 ( 65/32 ) +5

CalcPow

Calculate power

y=- 16 (4.12)+65 (65/32 )+5

Multiply

Multiply

y=- 65.99+132.01+5

AddTerms

Add terms

y=71.01

We have now identified the y-coordinate of the vertex of your throw. We can use the coordinates to compare your throw to that of your friend. Let's graph your vertex to visually show the difference.

Looking at the graph, we can estimate your friend's throw reached about 80 feet, whereas your throw only reached 71.01 feet. Therefore, the height of your throw is less than the height of your friend's throw.