Question

Analyze the key features of the graph of the quadratic function f(x) = –x^2 + 4x – 3.

1. Does the parabola open up or down?
2. Is the vertex a minimum or a maximum?
3. Identify the axis of symmetry, vertex and the y-intercept of the parabola.

Answer 1

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Answer:

1. down
2. maximum
3. x=2; (2, 1), -3

Explanation:

1. The negative leading coefficient (-2) tells you the parabola opens downward.

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2. The fact that the parabola opens downward tells you the vertex is a maximum.

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3. For quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For this parabola, that is x = -4/(2(-1)) = 2. The y-value of the vertex is f(2) = -2^2+4(2)-3 = -4+8-3 = 1. The y-intercept is the constant, c = -3.

• axis of symmetry: x = 2
• vertex: (2, 1)
• y-intercept: (0, -3)