Intercepts and Forms

Learn and apply intercepts and forms using equations, examples, and interpretation.

Lesson 3 of 53 parts Practice Flashcards

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Factored Form

Objective: Explain and use factored form in an Algebra 1 problem.

y=a(x−r₁)(x−r₂) exposes real zeros r₁ and r₂ when those factors exist. The graph touches the axis at a repeated root.

Worked examples

Try itExample 1.1: For y=(x−3)(x−5), what is the y-intercept?Show answer

15. Set x=0 to find the y-intercept. The answer is 15.

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Factored Form

Objective: Explain and use factored form in an Algebra 1 problem.

y=a(x−r₁)(x−r₂) exposes real zeros r₁ and r₂ when those factors exist. The graph touches the axis at a repeated root.

Worked examples

Try itExample 1.1: For y=(x−3)(x−5), what is the y-intercept?Show answer

15. Set x=0 to find the y-intercept. The answer is 15.

Quadratic Standard Form

Objective: Explain and use quadratic standard form in an Algebra 1 problem.

y=ax²+bx+c exposes the y-intercept (0,c), since all terms containing x vanish at zero. Only if x=0 is meaningful in the domain.

Worked examples

Try itExample 2.1: For y=(x−4)(x−8), what is the y-intercept?Show answer

32. Set x=0 to find the y-intercept. The answer is 32.

Converting Quadratic Forms

Objective: Explain and use converting quadratic forms in an Algebra 1 problem.

Expansion and factoring can reveal different features of one quadratic; equivalent forms yield the same outputs on their common domain. It makes the turning point easy to read.

Worked examples

Try itExample 3.1: For y=(x−2)(x−11), what is the y-intercept?Show answer

22. Set x=0 to find the y-intercept. The answer is 22.

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