Rewrite y = 2x^2 - 8x + 3 in vertex form and identify the vertex.

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $25.99Unlock all

Study for the Algebra 2 Honors Test. Prepare with flashcards and multiple choice questions, each question comes with hints and detailed explanations. Excel in your exam preparation!

Multiple Choice

Rewrite y = 2x^2 - 8x + 3 in vertex form and identify the vertex.

Explanation:
To rewrite a quadratic in vertex form, complete the square. Start with y = 2x^2 − 8x + 3 and factor out the 2 from the x-terms: y = 2(x^2 − 4x) + 3. Turn x^2 − 4x into a perfect square by adding and subtracting 4 inside the brackets: x^2 − 4x = (x − 2)^2 − 4. So y = 2[(x − 2)^2 − 4] + 3 = 2(x − 2)^2 − 8 + 3 = 2(x − 2)^2 − 5. This is in the form a(x − h)^2 + k, giving a = 2, h = 2, k = −5, so the vertex is (2, −5). You can also verify with h = −b/(2a) = 2 and k = f(2) = −5.

To rewrite a quadratic in vertex form, complete the square. Start with y = 2x^2 − 8x + 3 and factor out the 2 from the x-terms: y = 2(x^2 − 4x) + 3. Turn x^2 − 4x into a perfect square by adding and subtracting 4 inside the brackets: x^2 − 4x = (x − 2)^2 − 4. So y = 2[(x − 2)^2 − 4] + 3 = 2(x − 2)^2 − 8 + 3 = 2(x − 2)^2 − 5. This is in the form a(x − h)^2 + k, giving a = 2, h = 2, k = −5, so the vertex is (2, −5). You can also verify with h = −b/(2a) = 2 and k = f(2) = −5.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy