2.6P: Practice

MTH 95: Algebra 3 · LibreTexts

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    From LibreTexts, under CC BY-NC 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Practice Makes Progress

    Factor the given quadratic polynomial.

    Exercise

    \(x^2+9x+14\)

    Exercise

    \(x^2−4x−5\)

    Exercise

    \(x^2−7x+12\)

    Exercise

    \(5x^2−19x+12\)

    Exercise

    \(−4x^2+9x−5\)

    Exercise

    \(2x^2−3x−35\)

    Find the zeros of the given quadratic function.

    Exercise

    \(f(x) = x^2−2x−15\)

    Exercise

    \(f(x) = x^2+10x−39\)

    Exercise

    \(f(x) = 3x^2−20x+12\)

    Exercise

    \(f(x) = −4x^2+4x+15\)

    Perform each of the following tasks for the given quadratic function.

    1. Set up a coordinate system on graph paper. Label and scale each axis. Remember to draw all lines with a ruler.
    2. Use the technique of completing the square to 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.
    3. Use a strictly algebraic technique (no calculators) to find the x-intercepts of the graph of the given quadratic function. Plot them on your coordinate system and label them with their coordinates.
    4. Find the y-intercept of the graph of the quadratic function. Plot the y-intercept on your coordinate system and its mirror image across the axis of symmetry, then label these points with their coordinates.
    5. Using all the information plotted, draw the graph of the quadratic function and label it with the vertex form of its equation. Use interval notation to describe the domain and range of the quadratic function.
    Exercise

    \(f(x) = x^2+2x−8\)

    Exercise

    \(f(x) = −2x^2−4x+16\)

    Exercise

    \(f(x) = 3x^2+18x−48\)

    Solve the inequality. Write the solution in interval notation.

    Exercise

    \(x^2-9x+18>0\)

    Exercise

    \(4x^2+11x-20\geq 0\)

    Exercise

    \(-4x^2+7x\geq 0\)

    Exercise

    \(x^2-12x+36<0\)

    Self-Check

    In this section, you practiced:

    1. Factoring quadratic expressions with \(a = 1\)
    2. Factoring quadratic expressions with \(a \ne 1\)
    3. Finding \(x\)-intercepts of quadratic functions by factoring
    4. Graphing quadratic functions by finding the vertex, \(x\)-intercepts, and \(y\)-intercept

    From the list of skills above:

    1. I can complete these independently without notes:
    1. I can complete these, but need to reference an example or other resource to help:
    1. 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?

    This page titled 2.6P: Practice was last modified on Fri, 29 Aug 2025 03:30:39 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Math Department.