SAT Math: Practice Questions-Passport to advanced mathematics- Graphing quadratic functions

Question

For the quadratic function \(f\), the table shows some values of x and their corresponding values of  \(f(x)\). Which of the following could be the graph of \(y=f(x)\)?

 \(x\)         -1  0  1
f(\(x\))     0 -4  0      

Answer/Explanation

Ans: A

Question

What is the \(y\)-intercept of the graph of \(y\)=(\(x\)−4)2+3 in the \(xy\)-plane?

  1. (0,−13)
  2. (0,0)
  3. (0,3)
  4. (0,19)
Answer/Explanation

Ans: D

Question

\(y\)=(\(x\)+5)2-8

The equation above can be represented by a parabola in the \(xy\)-plane. The parabola is then translated so that the vertex is at (O, O). Which of the following best describes the translation? 

  1. 5 units in the negative \(x\) direction and 8 units in the negative \(y\) direction
  2. 5 units in the negative \(x\) direction and 8 units in the positive \(y\) direction
  3. 5 units in the positive \(x\) direction and 8 units in the negative \(y\) direction
  4. 5 units in the positive \(x\) direction and 8 units in the positive \(y\) direction
Answer/Explanation

Ans: D

Question

The graph of the function \(f\) defined by \(f(x)=\frac{1}{4}(x+4)^{2}-5\) is shown. The graph passes through the points (-10, \(a\)) and (\(a\), \(b\)), where \(a\) and \(b\) are constants. What is the value of \(b\) ? 

  1. 4
  2. 9
  3. 11
  4. 16
Answer/Explanation

Ans: C

Question

The graph of \(y\) = \(a\)\(x\)2 + \(c\), where \(a\) and \(c\) are constants, is shown. What is the value of \(a\) ? 

Answer/Explanation

Ans: .25, 1/4

Question

A potter is selling vases. The function \(p\) gives the total profit \(p(x)\), in dollars, the potter will receive if the vases are sold at a price of \(x\) dollars each. The graph of \(y = p(x)\) is shown. 

What equation represents the relationship between the price of one vase and the profit?

  1. \(p(x)=-6(x-18)^{2} +34\)
  2. \(p(x) = -6(x – 18)^{2} + 1536\)
  3. \(p(x) = -6(x – 34)^{2}+ 18\)
  4. \(p(x) = -6(x – 34)^{2}+ 1536\)
Answer/Explanation

Ans: B

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