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Question 12





x

g(x)


-6
0


-4
-12


-2
-16


0
-12


2
0


4
20




A quadratic function, 
f(x), is described by the equation 
f(x)=x^(2)+4x-10.
Some of the values of a second quadratic function, 
g(x), are shown in the table.
Which statement is a true comparison of the properties of 
f(x) and 
g(x) ?
The graph of 
g(x) has a lower minimum value and a lower 
y-intercept value than the graph of 
f(x).
The graph of 
g(x) has a higher minimum value but a lower 
y-intercept than the graph of 
f(x).
The graph of 
g(x) has a lower minimum value and a higher 
y-intercept value than the graph of 
f(x).
The graph of 
g(x) has a higher minimum value and a higher 
y-intercept value than the graph of 
f(x).

Question 1212\newlinexx\newlineg(x)g(x)\newline6-6\newline00\newline4-4\newline12-12\newline2-2\newline16-16\newline00\newline12-12\newlineg(x)g(x)00\newline00\newlineg(x)g(x)22\newlineg(x)g(x)33\newlineA quadratic function, \newlineg(x)g(x)44, is described by the equation \newlineg(x)g(x)55.\newlineSome of the values of a second quadratic function, \newlineg(x)g(x), are shown in the table.\newlineWhich statement is a true comparison of the properties of \newlineg(x)g(x)44 and \newlineg(x)g(x) ?\newlineThe graph of \newlineg(x)g(x) has a lower minimum value and a lower \newline6-600-intercept value than the graph of \newlineg(x)g(x)44.\newlineThe graph of \newlineg(x)g(x) has a higher minimum value but a lower \newline6-600-intercept than the graph of \newlineg(x)g(x)44.\newlineThe graph of \newlineg(x)g(x) has a lower minimum value and a higher \newline6-600-intercept value than the graph of \newlineg(x)g(x)44.\newlineThe graph of \newlineg(x)g(x) has a higher minimum value and a higher \newline6-600-intercept value than the graph of \newlineg(x)g(x)44.

Full solution

Q. Question 1212\newlinexx\newlineg(x)g(x)\newline6-6\newline00\newline4-4\newline12-12\newline2-2\newline16-16\newline00\newline12-12\newlineg(x)g(x)00\newline00\newlineg(x)g(x)22\newlineg(x)g(x)33\newlineA quadratic function, \newlineg(x)g(x)44, is described by the equation \newlineg(x)g(x)55.\newlineSome of the values of a second quadratic function, \newlineg(x)g(x), are shown in the table.\newlineWhich statement is a true comparison of the properties of \newlineg(x)g(x)44 and \newlineg(x)g(x) ?\newlineThe graph of \newlineg(x)g(x) has a lower minimum value and a lower \newline6-600-intercept value than the graph of \newlineg(x)g(x)44.\newlineThe graph of \newlineg(x)g(x) has a higher minimum value but a lower \newline6-600-intercept than the graph of \newlineg(x)g(x)44.\newlineThe graph of \newlineg(x)g(x) has a lower minimum value and a higher \newline6-600-intercept value than the graph of \newlineg(x)g(x)44.\newlineThe graph of \newlineg(x)g(x) has a higher minimum value and a higher \newline6-600-intercept value than the graph of \newlineg(x)g(x)44.
  1. Calculate y-intercept: Calculate the y-intercept of f(x)f(x) by substituting x=0x = 0 into the equation f(x)=x2+4x10f(x) = x^2 + 4x - 10.
  2. Find vertex for minimum value: Identify the minimum value of f(x)f(x) by finding the vertex of the parabola. The xx-coordinate of the vertex is given by b2a-\frac{b}{2a} for ax2+bx+cax^2 + bx + c.
  3. Identify g(x)g(x) y-intercept: Examine the values of g(x)g(x) from the table to find the y-intercept, which is g(0)g(0).
  4. Determine g(x)g(x) minimum value: Determine the minimum value of g(x)g(x) by checking the lowest yy-value in the table provided.
  5. Compare f(x)f(x) and g(x)g(x): Compare the y-intercepts and minimum values of f(x)f(x) and g(x)g(x).

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