orsion 2 You can earn: You can earn: 3-5: Answer all questions, showing any relevant work. you can see the vertex or showing the work you did to find it your answer for d should be based on your answer for a) 3. a) enthe graph to the right a) What is the vertex? b) How do you know? c) Is this a maximum or a minimum? d) What is the equation for the axis of symmetry? 4. Given the table to the right a) What is the vertex? b) How do you know? c) Is this a maximum or a minimum? d) What is the equation for the axis of symmetry? 5. Given the equation to the right a) What is the vertex? b) How do you know? c)Is this a maximum or a minimum? d) What is the equation for the axis of symmetry? f(x)=-3x^2+12x-8

Let's address each question one by one.<br /><br />### Question 3<br />Given the graph to the right:<br /><br />a) **What is the vertex?**<br /> - To answer this, we need to look at the graph and identify the highest or lowest point on the parabola. The vertex is either the maximum or minimum point of the graph.<br /><br />b) **How do you know?**<br /> - The vertex can be identified visually as the point where the parabola changes direction. If the parabola opens upwards, the vertex is the minimum point. If it opens downwards, the vertex is the maximum point.<br /><br />c) **Is this a maximum or a minimum?**<br /> - This depends on the direction in which the parabola opens. If the parabola opens upwards (like a U), the vertex is a minimum. If it opens downwards (like an upside-down U), the vertex is a maximum.<br /><br />d) **What is the equation for the axis of symmetry?**<br /> - The axis of symmetry is a vertical line that passes through the vertex. Its equation is \( x = h \), where \( h \) is the x-coordinate of the vertex.<br /><br />### Question 4<br />Given the table to the right:<br /><br />\[<br />\begin{array}{|c|c|}<br />\hline<br />x & f(x) \\<br />\hline<br />-4 & 6 \\<br />\hline<br />-3 & 3 \\<br />\hline<br />-2 & 2 \\<br />\hline<br />-1 & 3 \\<br />\hline<br />\end{array}<br />\]<br /><br />a) **What is the vertex?**<br /> - By examining the table, we see that \( f(x) \) decreases from 6 to 2 and then increases back to 3. Therefore, the vertex is at \( (-2, 2) \).<br /><br />b) **How do you know?**<br /> - The vertex is the point where the function changes direction from decreasing to increasing. In this case, \( f(x) \) reaches its minimum value at \( x = -2 \).<br /><br />c) **Is this a maximum or a minimum?**<br /> - Since \( f(x) \) changes from decreasing to increasing at \( x = -2 \), the vertex is a minimum.<br /><br />d) **What is the equation for the axis of symmetry?**<br /> - The axis of symmetry is the vertical line that passes through the vertex. Thus, the equation is \( x = -2 \).<br /><br />### Question 5<br />Given the equation to the right:<br /><br />\[ f(x) = -3x^2 + 12x - 8 \]<br /><br />a) **What is the vertex?**<br /> - To find the vertex of a quadratic function in the form \( ax^2 + bx + c \), use the formula \( x = -\frac{b}{2a} \).<br /> Here, \( a = -3 \), \( b = 12 \), and \( c = -8 \).<br /> \[<br /> x = -\frac{12}{2(-3)} = -\frac{12}{-6} = 2<br /> \]<br /> Now, substitute \( x = 2 \) back into the function to find \( f(2) \):<br /> \[<br /> f(2) = -3(2)^2 + 12(2) - 8 = -3(4) + 24 - 8 = -12 + 24 - 8 = 4<br /> \]<br /> So, the vertex is \( (2, 4) \).<br /><br />b) **How do you know?**<br /> - The vertex was found using the vertex formula \( x = -\frac{b}{2a} \) and substituting back into the function to find the corresponding \( y \)-value.<br /><br />c) **Is this a maximum or a minimum?**<br /> - Since the coefficient of \( x^2 \) (which is \( a = -3 \)) is negative, the parabola opens downwards, making the vertex a maximum.<br /><br />d) **What is the equation for the axis of symmetry?**<br /> - The axis of symmetry is the vertical line that passes through the vertex. Thus, the equation is \( x = 2 \).