Common Core Standard HSF-IF.C.8 Questions

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Grade 10 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

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Complete the square so that the function

$h(t)$ is in vertex form. Which of the following is correct? Round computed coefficients and terms to one decimal place, if necessary.

$h(t) = -4.9(t - 3.1)^2 - 9.4$
$h(t) = -4.9(t - 3.1)^2 + 45.9$
$h(t) = (-4.9t + 15)^2 - 225$
$h(t) = -4.9(t + 3.1)^2 + 9.4$

Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

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Find the percent rate of change for the function

$T(t)$ between

$t=1$ and

$t=2$ .

1.0%
9.0%
4.5%
95.5%

Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

Convert the quadratic function

$f(x) = x^2 - 10x + 25$ into vertex form and identify the vertex.

$Vertex: (-5, 0)$
$Vertex: (-5, 25)$
$Vertex: (5, 25)$
$Vertex: (5, 0)$

Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

What are the zeros of the function

$f(x)=x^2+2x−15$ ?

$Zeros: x=−3,5$
$Zeros: x=−5,3$
$Zeros: x=1 ,-15$
$Zeros: x=−1, 15$

Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

What are the x-intercepts of the quadratic function

$f(x)=x^2−6x+9$ ?

Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

Convert the quadratic function

$f(x)=3x^2+12x+7$ into vertex form by completing the square, and find the vertex.

Vertex: (2,5)
Vertex: (-2,2)
Vertex: (3,1)
Vertex: (-2,-5)

Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

Factor the quadratic function

$f(x)=x^2+5x+6$ and find the zeros.

x=2,3
x=-2,-3
x=-1, 5
x=1,6

Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

If $5,000 is invested at 8% interest compounded semi-annually, what function models the investment after t years?

$A(t)=5000(1+0.08)^(2t)$
$A(t)=5000(1+0.08/2)^(2t)$
$A(t)=5000(1+0.04)^(2t)$
$A(t)=5000(1+0.08)^(t)$

Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

Simplify

$f(x)=(2^x)(8^(-x/2))$ , and find the percent rate of change.

50%, decay
75%, growth
0%
Constant function

Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

Given two accounts: one with 6% interest compounded annually, and another with 6% interest compounded semi-annually, which account has the higher effective rate of change?

Account I (annually)
Account II (semi-annually)
Both have the same rate
Cannot be determined

Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b

What is the percent rate of change for the function

$f(x)=200(1.09)^t$ ?

9%, growth
0.9%, growth
90%, growth
1.09%, growth

Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b

Given the compound interest function

$A(t)=2000(1+0.034)^(4t$ , what is the interest rate, and how often is it compounded?

3%, quarterly
12%, annually
3%, annually
4%, quarterly

Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b

The function

$y = (1.005)^(12t$ represents interest compounded monthly. What is the annual percent rate of growth?

6%
5%
0.5%
12%

Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b

Given

$f(t) = 800(0.9)^t$ , does the function represent exponential growth or decay, and what is the rate of change?

10%, growth
10%, decay
90%, growth
0.9%, decay

Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b

$h(x) = (⅓) (1.5)^x$ , what type of change does the function represent?

Exponential growth
Exponential decay
Constant
Linear growth

Grade 10 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

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What facts about the rocket can be seen directly from the vertex form of the function? Choose all that apply.

The time when the rocket reached its maximum height.
The total duration of the rocket's flight.
The initial velocity of the rocket.
The rocket's maximum height.

Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

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Why are the numbers for the percent rate of change calculated in the previous two questions not the same?

Because the calculations didn't use exact numbers, and therefore there are rounding errors.
Because the function has an added constant (it is not of the form $ab^x$ ).
Because the percent rate of change calculated from the different form of the function, $T(t) = a*b^t + c$ , is a general rate of change, which is not the same as the specific rate of change from $t=1$ to $t=2$ .
Because an exponential function is not constant, therefore its percent rate of change shouldn't be constant.

Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

Complete the square for

$f(x) = x^2 + 4x + 1$ , then find the vertex.

$Vertex: (-2, -3)$
$Vertex: (2, 1)$
$Vertex: (-2, -1)$
$Vertex: (-2, -5)$

Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

Factor the quadratic function and find the x-intercepts:

$f(x)=2x^2−8x$

Grade 11 Quadratic Equations and Expressions CCSS: HSF-IF.C.8, HSF-IF.C.8a

Factor

$f(x)=x^2−5x+6$ , and find the zeros.

Zeros: 2,3
Zeros: -2,3
Zeros: 1,6
Zeros: 2,-3

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Common Core Standard HSF-IF.C.8 Questions

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