[discia] GCSE Maths › Algebra › Drawing Quadratic Graphs

Drawing Quadratic Graphs

discia.org 10 questions · 28 marks
Name Date
  1. Either paper 3 marks

    The graph of \(y = x^2 - 6x + 5\) is drawn on the grid.

    1234567-7-6-5-4-3-2-11234560xy
    (a)

    Write down the two values of \(x\) where the curve crosses the \(x\)-axis.

    (b)

    Write down the coordinates of the point where the curve crosses the \(y\)-axis.

    Show answer
    (a) \(x = 1\) and \(x = 5\)
    (b) \((0, 5)\)
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  2. Either paper 3 marks
    The table shows some values of \(y = x^2 + 2x \)
    x-4-3-2-1012
    y30-108
    Two of the \(y\) values are missing.
    (a)

    Work out the value of \(y\) when \(x = -4\).

    (b)

    Work out the value of \(y\) when \(x = 1\).

    (c)

    Write down the coordinates of the lowest point shown in the table.

    Show answer
    (a) \(8\)
    (b) \(3\)
    (c) \((-1, -1)\)
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  3. Either paper 2 marks

    The graph of \(y = x^2 - 2x \) is drawn on the grid.

    -4-3-2123456-3-21234567891011120xy
    (a)

    Write down the coordinates of the turning point of the curve.

    (b)

    Write down the equation of the line of symmetry of the curve.

    Show answer
    (a) \((1, -1)\)
    (b) \(x = 1\)
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  4. Either paper 3 marks

    The graph of \(y = x^2 - 8x + 7\) is drawn on the grid.

    123456789-11-10-9-8-7-6-5-4-3-212340xy
    (a)

    Use the graph to write down the value of \(y\) when \(x = 3\).

    (b)

    Use the graph to write down the two values of \(x\) when \(y = -5\).

    Show answer
    (a) \(-8\)
    (b) \(x = 2\) and \(x = 6\)
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  5. Either paper 2 marks
    Here is a table of values for \(y = x^2 - 2x - 3\)
    x-2-101234
    y50-3-4-305
    On the grid, draw the graph of \(y = x^2 - 2x - 3\) for values of \(x\) from \(-2\) to \(4\). -3-212345-6-5-4-3-2-11234560xy
    Show answer
    A smooth curve through the seven points of the table, with its lowest point at \((1, -4)\)
    -3-212345-6-5-4-3-2-11234560xy
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  6. Either paper 2 marks
    A student has filled in a table of values for \(y = x^2 - 6x \)
    x0123456
    y0-4-8-9-8-50
    One of the \(y\) values is wrong.
    (a)

    Write down the value of \(x\) for the entry that is wrong.

    (b)

    State the correct value of \(y\) for that entry.

    Show answer
    (a) \(1\)
    (b) \(-5\)
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  7. Either paper 2 marks

    The graph of \(y = x^2 + 6x + 8\) and the line \(y = 3\) are both drawn on the grid.

    -7-6-5-4-3-21-3-2-11234567890xy

    Use the graphs to solve \(x^2 + 6x + 8 = 3\)

    Show answer
    \(x = -5\) and \(x = -1\)
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  8. Either paper 3 marks

    The graph of \(y = -x^2 + 2x \) is drawn on the grid.

    Because of the minus sign in front of the \(x^2\), this parabola opens downwards.

    -2-11234-6-5-4-3-2-11230xy
    (a)

    Write down the coordinates of the highest point of the curve.

    (b)

    Write down the two values of \(x\) where the curve crosses the \(x\)-axis.

    Show answer
    (a) \((1, 1)\)
    (b) \(x = 0\) and \(x = 2\)
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  9. Either paper 5 marks

    A curve has equation \(y = (x + 3)(x - 5)\)

    It is a parabola, and it opens upwards.

    (a)

    Write down the two values of \(x\) where the curve crosses the \(x\)-axis.

    (b)

    Write down the equation of the line of symmetry of the curve.

    (c)

    Work out the minimum value of \(y\).

    Show answer
    (a) \(x = -3\) and \(x = 5\)
    (b) \(x = 1\)
    (c) \(-16\)
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  10. Either paper 3 marks
    Here is a table of values for \(y = 2x^2 - 10x - 1\)
    x-101234
    y11-1-9-13-13-9
    The graph of \(y = 2x^2 - 10x - 1\) is a parabola that opens upwards.
    (a)

    Write down the \(x\)-coordinate of the turning point of the graph.

    (b)

    Find the minimum value of \(y\).

    Show answer
    (a) \(\frac{5}{2}\)
    (b) \(-\frac{27}{2}\)
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discia.org Drawing Quadratic Graphs · sheet 1
Answers Drawing Quadratic Graphs · sheet 1
  1. (a) \(x = 1\) and \(x = 5\)
    (b) \((0, 5)\)
  2. (a) \(8\)
    (b) \(3\)
    (c) \((-1, -1)\)
  3. (a) \((1, -1)\)
    (b) \(x = 1\)
  4. (a) \(-8\)
    (b) \(x = 2\) and \(x = 6\)
  5. A smooth curve through the seven points of the table, with its lowest point at \((1, -4)\)
    -3-212345-6-5-4-3-2-11234560xy
  6. (a) \(1\)
    (b) \(-5\)
  7. \(x = -5\) and \(x = -1\)
  8. (a) \((1, 1)\)
    (b) \(x = 0\) and \(x = 2\)
  9. (a) \(x = -3\) and \(x = 5\)
    (b) \(x = 1\)
    (c) \(-16\)
  10. (a) \(\frac{5}{2}\)
    (b) \(-\frac{27}{2}\)
discia.org Drawing Quadratic Graphs · sheet 1