Algebra 1 Graphing Quadratic Functions and Transformations Quiz: 10 Questions with Explanations

A \((-5, 1)\)B \((5, 1)\)C \((5, -1)\)D \((1, 5)\)

In vertex form a(x – h)² + k, the vertex is (h, k). The minus sign in x – 5 means h = 5.

A \(x = -4\)B \(x = 1\)C \(x = -1\)D \(y = 1\)

The axis passes through the vertex (1, -4), so it is the vertical line x = 1.

A \(x = 5\)B \(x = 9\)C \(x = 4\)D \(x = 10\)

The axis is halfway between the x-intercepts: (1 + 9)/2 = 5.

A Wider and opening downB Narrower and opening upC Narrower and opening downD Shifted down 3 units

The factor 3 stretches the graph vertically, and the negative sign flips it.

A \(y = (x + 4)^{2}\)B \(y = (x – 4)^{2}\)C \(y = x^{2} + 4\)D \(y = x^{2} – 4\)

A left shift of 4 replaces x with x + 4.

A 1B 3C -1D 4

The maximum is the y-coordinate of the vertex, which is 4. The x-coordinate 1 is where it occurs.

A \(y = (x + 5)^{2} + 21\)B \(y = (x + 5)^{2} – 4\)C \(y = (x + 10)^{2} – 79\)D \(y = (x – 5)^{2} – 4\)

Add and subtract 25: (x² + 10x + 25) – 25 + 21 = (x + 5)² – 4.

A $10B $20C $500D $5

p = -b/(2a) = -100/(-10) = 10. The maximum revenue itself is $500.

A \((1, 0)\)B \((0, 3)\)C \((-1, 8)\)D \((2, -1)\)

The outputs at x = 1 and x = 3 are equal, so the axis is x = 2 and the vertex is (2, -1).

A \(x = -2\) and \(x = 6\)B \(x = 2\) and \(x = 6\)C \(x = 2\) and \(x = -6\)D \(x = -2\) and \(x = -6\)

Set each factor to 0: x – 2 = 0 and x + 6 = 0.