Graphing and Solving Systems of Equations

The video tutorial explains how to solve a system of equations by graphing. It begins with graphing a downward opening parabola and a linear equation. The tutorial then identifies the points of intersection between the two graphs, verifying the solutions algebraically. Key points include understanding the nature of quadratic and linear equations, graphing techniques, and finding intersections.

What type of graph is formed by a quadratic equation?

• A parabola

• A circle

• An ellipse

• A straight line

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CCSS.HSF-IF.C.7A

How can you determine if a parabola opens upwards or downwards?

• By the sign of the linear term

• By the sign of the x term

• By the sign of the constant term

• By the sign of the coefficient of the x-squared term

What is the vertex of the parabola y = -x^2 + 6?

• (0, 6)

• (0, 0)

• (6, 6)

• (6, 0)

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CCSS.HSF.IF.A.2

What is the y-coordinate when x = 2 for the equation y = -x^2 + 6?

• 4

• -2

• 2

• 0

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CCSS.8.EE.B.5

What is the slope of the line y = -2x - 2?

• -2

• 2

• -1

• 0

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CCSS.8.EE.B.6

CCSS.8.F.A.3

What is the y-intercept of the line y = -2x - 2?

• 0

• 2

• -1

• -2

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CCSS.HSA.REI.C.7

Which point is a solution to both the parabola and the line?

• (0, 6)

• (2, 2)

• (-2, 2)

• (4, -10)

What is the x-coordinate of the second intersection point of the parabola and the line?

• -2

• 4

• 2

• 0

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CCSS.HSA.REI.C.7

What is the y-coordinate of the second intersection point of the parabola and the line?

• -10

• -2

• 2

• 10

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

How can you verify that a point is a solution to both equations?

• By graphing the point

• By checking if it lies on the y-axis

• By substituting the point into both equations

• By checking if it lies on the x-axis

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6