Graph each inequality. y≥x2−9

Ch. 5 - Systems of Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

문제 21

6장, 문제 21

Graph each inequality. y≥x²−9

검증된 단계별 안내

Identify the inequality to be graphed: \(y \geq x^{2} - 9\). This means we are dealing with a parabola and the region above or on the parabola.

Start by graphing the boundary curve \(y = x^{2} - 9\). This is a parabola opening upwards with its vertex at the point \((0, -9)\).

Since the inequality is \(y \geq x^{2} - 9\), the boundary line (the parabola) is included in the solution set, so draw the parabola as a solid curve.

Determine which side of the parabola to shade by choosing a test point not on the parabola, commonly \((0,0)\), and check if it satisfies the inequality: substitute \(x=0\) and \(y=0\) into \(y \geq x^{2} - 9\).

If the test point satisfies the inequality, shade the region containing that point; if not, shade the opposite side. This shaded region represents all solutions to the inequality.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Graphing Quadratic Functions

A quadratic function is a polynomial of degree two, typically written as y = ax² + bx + c. Its graph is a parabola that opens upward if a > 0 and downward if a < 0. Understanding the shape and position of the parabola y = x² - 9 helps in sketching the boundary for the inequality.

Inequalities and Their Graphs

Graphing inequalities involves shading the region of the coordinate plane where the inequality holds true. For y ≥ x² - 9, the graph includes all points on or above the parabola y = x² - 9. The boundary curve is solid because the inequality includes equality (≥).

Boundary Lines and Shading Regions

The boundary line or curve separates the solution region from the non-solution region. For inequalities with '≥' or '≤', the boundary is included and drawn solid. After graphing the boundary, test points determine which side to shade, representing all solutions to the inequality.