The equation of the quadratic function in standard form as required in the task content is; f(x) = -x² + 12x - 43.
<h3>Standard form equation of a quadratic function.</h3>
It follows from the task content that the standard form equation of the quadratic function is to.be determined.
Since the standard form equation can be derived from the vertex form equation as follows;
f(x) = a (x - h)² + k
f(x) = a (x - 6)² - 7
Hence, to find the value of a, Substitute x = 8 and f(x) = -11 so that we have;
-11 = a (8 - 6)² - 7
-11 = 4a - 7
4a = -4
a = -1.
Hence, the equation in vertex form is; f(x) = -1 (x -6)² - 7 and when expressed in standard form we have;
f(x) = -1(x² - 12x + 36) - 7
f(x) = -x² + 12x - 43
Therefore, the required equation in standard form is; f(x) = -x² + 12x - 43.
Read more on quadratic functions;
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<span>Outcome Heads Tails
Relative Frequency 0.69 0.31
so first statement is false as 69% is close to 70%.
second statement is false as heads probability is close to 70%
last 2 statements are true:
</span><span>The theoretical probability of tails is most likely 30%.
It is likely that the coin is not fair.
</span>
Answer: 1 hour is equal to 46 miles 2 hours is 92 miles and 20 hours is 920 miles
Step-by-step explanation:
92/2 = 46 miles
46 x 2 = 92 miles
46 x 20 = 920
Answer:
49 inches
Step-by-step explanation:
To obtain the height, h of the ramp ;; we use trigonometry ;
h = opposite and the value of the hypotenus :
Sin θ = opposite / hypotenus
Sin 22 = h / 132
h = 132 * sin 22
h = 132 * 0.3746065
h = 49.44
Height of ramp = 49 inches
Answer:
Step-by-step explanation:
Hypotenuse = x
Base = 4
Perpendicular = 
<u>Using Pythagoras Theorem:</u>
![\sf H^2 = P^2 + B^2\\\\ x^2 = (\sqrt{84} )^2 + (4)^2\\\\x^2 = 84 + 16\\\\x^2 = 100\\\\Taking \ sq \ root \ on \ both \ sides\\\\x = 10\\\\\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Csf%20H%5E2%20%3D%20P%5E2%20%2B%20B%5E2%5C%5C%5C%5C%20x%5E2%20%3D%20%28%5Csqrt%7B84%7D%20%29%5E2%20%2B%20%284%29%5E2%5C%5C%5C%5Cx%5E2%20%3D%2084%20%2B%2016%5C%5C%5C%5Cx%5E2%20%3D%20100%5C%5C%5C%5CTaking%20%5C%20sq%20%5C%20root%20%5C%20on%20%5C%20both%20%5C%20sides%5C%5C%5C%5Cx%20%3D%2010%5C%5C%5C%5C%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
