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Question 1
Consider the function
f(x)=3x2+9x−12f of x equals 3 x squared plus 9 x minus 12.
Fill in the missing portions of the equation to rewrite f(x)f of x to reveal the vertex of the graph of the function. Use decimals or fractions as needed.
Answer:Correct! Go to question 2.Incorrect. The correct answer is:
f(x)=3(x+1.5)2+-negative18.75f of x equals 3 times the quantity of x plus one and five tenths squared plus negative 18 and 75 hundredths
[using fraction:
f(x)=3(x+1.5)2+-negative754]f of x equals 3 times the quantity of x plus one and five tenths squared plus negative seventy-five fourths
The quadratic function, f(x)=3x2+9x−12f of x equals 3 x squared plus 9 x minus 12, has a minimum value of -negative18.75 and has zeros at -negative4 and 1. The equation
f(x)=3(x+1.5)2+-negative18.75f of x equals 3 times the quantity of x plus one and five tenths squared plus negative 18 and 75 hundredths
is in vertex form, that is
y=a(x−h)2+ky equals a times the quantity x minus h squared plus k. The vertex is (h,k). This parabola opens upward since a is positive (a=3). Therefore, the vertex is a minimum. By setting the equation equal to zero, you can solve for the zeros.
Go to question 2.
Incorrect. Refer to the ‘Steps for Completing the Square’ in Review It to help you, and try again.