# 5.01 Key Properties of Quadratic Graphs

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5.01 Key Properties of Quadratic Graphs

Identify whether each of the following quadratic functions will be a positive or a negative parabola.

 1 f(x) = –x2 – 5x + 4 Positive or Negative: negative 2 f(x) = 2x2 + 8x + 16 Positive or Negative: positive 3 Positive or Negative: negative 4 f(x) = 7x2 + 22x + 3 Positive or Negative: positive

Identify each key feature of the parabola that has been graphed. You have also been given the equation of the parabola if you should happen to need it.

 5. Equation: f(x) = 3x2 – 18x + 24 Positive or Negative? Vertex (     ,      ) Axis of Symmetry x = Max or Mini & Point at (     ,      ) Increasing Interval (     ,      ) Decreasing Interval (     ,      ) x-intercepts (     ,      ) and (     ,      ) y-intercept (     ,      )

 6. Equation: y = –x2 – 6x – 10 Positive or Negative? Vertex (     ,      ) Axis of Symmetry x = Max or Mini & Point at (     ,      ) Increasing Interval (     ,      ) Decreasing Interval (     ,      ) x-intercepts (     ,      ) and (     ,      ) y-intercept (     ,      )

 7. Equation: f(x) = x2 + 6x + 5 Positive or Negative? Vertex (     ,      ) Axis of Symmetry x = Max or Mini & Point at (     ,      ) Increasing Interval (     ,      ) Decreasing Interval (     ,      ) x-intercepts (     ,      ) and (     ,      ) y-intercept (     ,      )

Using the given key features, sketch the graph. You will move the points, line, and curve to the correct position. Your curve should be the last thing on your drawing. You can turn it and stretch it as necessary.

8. Opens down

Vertex/Maximum Point at (-2, 3)

x-intercepts at (-3, 0) and (-1, 0)

Axis of Symmetry at x = -2

9. Opens up

Vertex/Minimum Point at (0, -2)

x-intercepts at (-3, 0) and (3, 0)

Axis of Symmetry at x = 0

10. Opens down

Vertex/Minimum Point at (1, 3)

x-intercepts at (-2, 0) and (4, 0)

Axis of Symmetry at x = 1

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