2.7P: Practice
- Page ID
- 192248
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Practice Makes Progress
Find all real solutions of the given equation. Use a calculator to approximate the answers, correct to the nearest hundredth.
\(x^2 = 36\)
\(x^2 = 17\)
\(x^2 = 0\)
\(x^2 = −12\)
\((x−1)^2 = 25\)
\((x+2)^2 = 0\)
\((x−8)^2 = 15\)
Perform each of the following tasks for the given quadratic function.
- Set up a coordinate system on a sheet of graph paper. Label and scale each axis. Remember to draw all lines with a ruler.
- Place the quadratic function in vertex form. Plot the vertex on your coordinate system and label it with its coordinates. Draw the axis of symmetry on your coordinate system and label it with its equation.
- Use the quadratic formula to find the x-intercepts of the parabola. Use a calculator to approximate each intercept, correct to the nearest tenth, and use these approximations to plot the x-intercepts on your coordinate system. However, label each x-intercept with its exact coordinates.
- Plot the y-intercept on your coordinate system and its mirror image across the axis of symmetry and label each with their coordinates.
- Using all of the information on your coordinate system, draw the graph of the parabola, then label it with the vertex form of the function. Use interval notation to state the domain and range of the quadratic function.
\(f(x) = x^2−4x−8\)
\(f(x) = −x^2+2x+10\)
Perform each of the following tasks for the given quadratic equation.
- Set up a coordinate system on a sheet of graph paper. Label and scale each axis. Remember to draw all lines with a ruler.
- Show that the discriminant is negative.
- Use the technique of completing the square to put the quadratic function in vertex form. Plot the vertex on your coordinate system and label it with its coordinates. Draw the axis of symmetry on your coordinate system and label it with its equation.
- Plot the y-intercept and its mirror image across the axis of symmetry on your coordinate system and label each with their coordinates.
- Because the discriminant is negative (did you remember to show that?), there are no x-intercepts. Use the given equation to calculate one additional point, then plot the point and its mirror image across the axis of symmetry and label each with their coordinates.
- Using all of the information on your coordinate system, draw the graph of the parabola, then label it with the vertex form of function. Use interval notation to describe the domain and range of the quadratic function.
\(f(x) = x^2+4x+8\)
\(f(x) = −x^2+6x−11\)
Find all values of \(k\) so that the graph of the quadratic function given has exactly two \(x\)-intercepts (hint: use the discriminant).
\(f(x) = kx^2−3x+5\)
\(f(x) = 2x^2−x+5k\)
Find all real solutions, if any, of the quadratic equation.
\(x^2−2 = −3x\)
\(9x^2+81 = −54x\)
Find all of the x-intercepts, if any, of the given function.
\(f(x) = −4x^2−4x−5\)
\(f(x) = −56x^2+47x+18\)
In this section, you practiced:
- Solving quadratic equations using the square root method
- Solving quadratic equations using the quadratic formula
- Graphing quadratic equations by finding the vertex, \(x\)-intercepts, and \(y\)-intercept
- Using the discriminant to determine the number of \(x\)-intercepts of a quadratic function
From the list of skills above:
- I can complete these independently without notes:
- I can complete these, but need to reference an example or other resource to help:
- I don’t understand these yet:
It’s okay to not be fully confident with every skill yet! But it’s essential to continue making progress. Identify at least one step you will take to improve your understanding of the topics you listed in parts 2 or 3 above:
- Visit the math lab
- Contact my instructor
- Re-work practice problems
- Ask a classmate or friend for help
Which step(s) from above did you complete after last week's textbook practice?