Lesson 10 Graphs of Functions in Standard and Factored Form

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9th - 12th grade

Mathematics

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Lesson 10 Graphs of Functions in Standard and Factored Form

Body text

What are the x-intercepts of the graph of the function defined by (x−2)(2x+1)?

answer choices

(2,0) and (-1,0)

(2,0) and (-1/2,0)

(-2,0) and (1,0)

(2,0) and (1/2,0)

$y=x^2-5x+4$ What is the y-intercept of the equation?

List your answer as a point with no spaces ex(-5,2)

answer

(0,4)

An equivalent way to write this equation is y=(x−4)(x−1). What are the x-intercepts of this equation’s graph?

answer choices

(-4,0) and (-1,0)

(4,0) and (1,0)

(0,-4) and (0,-)

(0,4) and (0,-1)

answer choices

Write each quadratic expression in standard form. Draw a diagram if needed.

(x−3)(x−6)

answer choices

$x^2-3x-6$

$x^2-9x-18$

$x^2-3x-6$

$x^2+18$

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">x^2-3x-6</annotation></semantics></math>x2−3x−6

alternatives

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>9</mn><mi>x</mi><mo>−</mo><mn>18</mn></mrow><annotation encoding="application/x-tex">x^2-9x-18</annotation></semantics></math>x2−9x−18

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>3</mn><mi>x</mi><mo>−</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">x^2-3x-6</annotation></semantics></math>x2−3x−6

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>18</mn></mrow><annotation encoding="application/x-tex">x^2+18</annotation></semantics></math>x2+18

Write each quadratic expression in standard form. Draw a diagram if needed.

\left(x-4\right)^2

answer choices

$x^2+8x-16$

$x^2-8x+16$

$x^2-4x-4$

$x^2+16$

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>x</mi><mo>−</mo><mn>16</mn></mrow><annotation encoding="application/x-tex">x^2+8x-16</annotation></semantics></math>x2+8x−16

alternatives

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>8</mn><mi>x</mi><mo>+</mo><mn>16</mn></mrow><annotation encoding="application/x-tex">x^2-8x+16</annotation></semantics></math>x2−8x+16

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">x^2-4x-4</annotation></semantics></math>x2−4x−4

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn></mrow><annotation encoding="application/x-tex">x^2+16</annotation></semantics></math>x2+16

Write each quadratic expression in standard form. Draw a diagram if needed.

(2x+3)(x−4)

answer choices

$2x^2-5x-12$

$2x^2-x-1$

$2x^2-4x-12$

$x^2+16$

<math><semantics><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>5</mn><mi>x</mi><mo>−</mo><mn>12</mn></mrow><annotation encoding="application/x-tex">2x^2-5x-12</annotation></semantics></math>2x2−5x−12

alternatives

<math><semantics><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mi>x</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">2x^2-x-1</annotation></semantics></math>2x2−x−1

<math><semantics><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>12</mn></mrow><annotation encoding="application/x-tex">2x^2-4x-12</annotation></semantics></math>2x2−4x−12

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn></mrow><annotation encoding="application/x-tex">x^2+16</annotation></semantics></math>x2+16

Write each quadratic expression in standard form. Draw a diagram if needed.

(4x−1)(3x−7)

answer choices

$12x^2-31x+7$

$12x^2-3x+7$

$x^2-4x-7$

$12x^2+7$

<math><semantics><mrow><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>31</mn><mi>x</mi><mo>+</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">12x^2-31x+7</annotation></semantics></math>12x2−31x+7

alternatives

<math><semantics><mrow><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">12x^2-3x+7</annotation></semantics></math>12x2−3x+7

<math><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">x^2-4x-7</annotation></semantics></math>x2−4x−7

<math><semantics><mrow><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">12x^2+7</annotation></semantics></math>12x2+7