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13 Cards in this Set
- Front
- Back
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What are the steps to factoring a quadratic expression to reveal the zeroes of the function it defines?
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To factor a quadratic, first be sure it is in quadratic form ax2+bx+c=0. Next, you need to find a pair of factors with a product that is equal to c and a sum that is equal to b. Use these to factors as terms so that x plus one factor equals zero and x plus the other factor equals zero, then solve for x.
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Factor this quadratic expression to find the zeroes of the function. k²+29k=0
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k²+29k=0
k(k+29)=0 k=0 k+29=0 k=0 k=-29 |
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Factor this quadratic expression to find the zeroes of the function. x²+30x+125=0
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x²+30x+125=0
(x+5)(x+25)=0 x+5=0 x+25=0 x=-5 x=-25 |
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Factor this quadratic expression to find the zeroes of the function. x²-13x-30=0
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x²-13x-30=0
(x-15)(x+2)=0 x-15=0 x+2=0 x=15 x=-2 |
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What are the steps to completing the square in a quadratic equation to reveal the maximum or minimum value of the function it defines
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To complete the square in a quadratic equation, first ensure that the equation is in ax2+bx+c form, then move the c term to the opposite sign of the equal sign. Next, divide all terms by the a term. Then, take half of the coefficient of the middle term, square it, and add that value to both sides of the equation. Now, factor the perfect square trinomal and solve to find the roots.
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Complete the square to find the maximum or minimum value of the quadratic function. x²-6x+8=0
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x²-6x+8=0
x²-6x=-8 x²-6x+(½*-6)²=-8+(½*-6)² x²-6x+9=-8+9 (x-3)(x-3)=1 √(x-3)²=±√1 x-3=±1 x-3=1 x-3=-1 x=4 x=2 |
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Complete the square to find the maximum or minimum value of the quadratic function. 2x²-6x+3=0
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2x²-6x+3=0
2x²-6x=-3 2x²/2-6x/2=-3/2 x²-3x=-3/2 x²-3x+(½*-3)²=-3/2+(½*-3)² x²-3x+9/4=-3/2+9/4 (x-3/2)²=¾ √(x-3/2)²=±√¾ x-3/2=±(√3)/2 x=3/2+(√3)/2 x=3/2-(√3)/2 |
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Complete the square to find the maximum or minimum value of the quadratic function. x²-8x+24=0
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x²-8x+24=0
x²+8x=-24 x²-8x+(½*-4)²=-24+(½*-4)² x²-8x+16=-24+16 (x-4)²=-8 √(x-4)²=±√-8 x-4=±2i√2 x=4±2i√2 x=4+2i√2 x=4-2i√2 |
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Transform the expression 1.15^t to reveal the approximate monthly interest rate if the annual rate is 15%.
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(1.15^1/12)^12t ≈ 1.012^12t
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What is the formula for the nth term of a geometric sequence?
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aⁿ= a₁rⁿ⁻¹ where aⁿ is the nth term, a₁ is the first term, r is the common ratio and n is the position of a term in the sequence.
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Write an equation to describe the sequence -4, -16, -64,.... using n to represent the position of a term in the sequence, where n=1 for the first term.
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aⁿ= -4(4)ⁿ⁻¹
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What type of series is the monthly mortgage payment formula derived from?
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The monthly mortgage payment formual is derived from the sum of a finite geometric series.
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Bob took out a $125,000 mortgage at 8.75% with an amortization period of 25 years. Calculate the monthly payments using the formula P = L * c(1+c)ⁿ / (1+cⁿ)-1
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P = L * c(1+c)ⁿ / (1+cⁿ)-1
P= (125000) * [(0.0875/12)*(1+0.0875/12)³⁰⁰/((1+0.0875/12)³⁰⁰-1)] P=$1027.67 |
