Which is the slope intercept form of an equation for the line containing (0,-3) woth slope -1?
1 answer:
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The function of the path of the punted ball is a quadratic function which
follows the path of a parabola.
The correct responses are;
Part A: The coordinates of the vertex is
Part B: The maximum height of the punt is <u>36.81 ft.</u>
Part C: The defensive player must reach up to <u>7.65 feet</u> to block the punt.
Part D: The distance down the field the ball will go without being blocked is approximately <u>119.67 ft.</u>
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Reasons:
The function for the height of the punted ball is; h = -0.01·x² + 1.18·x + 2
Assumption; The distances are feet.
Part A: By completing the square, we have;
f(x) = -0.01·x² + 1.18·x + 2
100·f(x) = -x² + 118·x + 200
-100·f(x) = x² - 118·x - 200
x² - 118·x + (118/2)²= 200 + (118/2)²
(x - 59)² = 200 + (59)² = 3681
(x - 59)² - 3681
At the vertex, -3281 = -100·f(x)
∴ f(x) at the vertex = -3681/-100 = 36.81
Part B: The maximum height is given by the y-value at the vertex = 36.81 ft.
Part C: When <em>x</em> = 5, we have;
h = -0.01·x² + 1.18·x + 2
h = -0.01 × 5² + 1.18 × 5 + 2 = 7.65
The defensive player must reach up to 7.65 feet to block the punt
Part D: The distance the ball will go before it hits the ground is given by
the function, for the height as follows;
h = -0.01·x² + 1.18·x + 2 = 0
From the completing the square method, above, we get;
-0.01·x² + 1.18·x + 2 = 0
x² - 118·x - 200 = 0
x² - 118·x + (118/2)²= 200 + (118/2)²
x² - 118·x + (59)²= 200 + (59)² = 3681
(x - 59)² = 3681
x - 59 = ±√3681
x = 59 ± √3681
x = 59 + √3681 ≈ 119.67
The distance down the field the ball will go without being blocked, x ≈ <u>119.67 ft.</u>
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Answer:
Step-by-step explanation:
a = 2, b = 1, c = -3
We need to factor this by finding the product of a and c, then from there find which factors of a * c will either add or subtract to give us b.
a * c = 6 and the factors of 6 and 1 and 6, 2 and 3. Well, 6 - 1 doesn't equal 1 and neither does 6 + 1. So our factors are 3 and 2. In order to combine those to get a 1 (our b), we will subtract 2 from 3 since 3 - 2 = 1. That means that 3 is positive and 2 is negative. Filling in the formula with 3 and 2 in place of 1 looks like this (always remember to put the absolute value of the largest number first):
Group the first 2 terms together and the second 2 term together in order to factor:
and factor out what's common in each set of parenthesis.
Notice that when we factor out a -1 from the second set of parenthesis, we can distribute it back in to get the equation we started with. We know that factoring by grouping "works" if what is inside both sets of parenthesis is exactly the same. Ours are identical: (2x + 3). That is common now, and can be factored out:
That matches your first choice