Exploring Quadratic Equations through Graphing

What method of solving quadratics is introduced in Chapter 9?

• Solving by elimination

• Solving by graphing

• Solving by decomposition

• Solving by substitution

How many solutions does a quadratic equation have if it touches the x-axis once?

• One solution

• Two solutions

• Infinite solutions

• No solutions

What does it mean if a quadratic graph crosses the x-axis at two points?

• The equation has one solution

• The equation cannot be solved

• The equation has two solutions

• The equation has no solution

What are the solutions for the equation x^2 - 3x - 10 = 0 when solved by graphing?

• x = -5 and x = -2

• x = -5 and x = 2

• x = 5 and x = 2

• x = 5 and x = -2

What is the correct factorization of x^2 - 3x - 10?

• (x + 5)(x - 2)

• (x - 5)(x + 2)

• (x - 5)(x - 2)

• (x + 5)(x + 2)

What should you always do after finding potential solutions on a graph?

• Check the solutions in the original equation

• None of the above

• Solve the equation by factoring

• Graph the equation again

What is the result of graphing the equation x^2 + 8x = -16?

• x = -8

• x = 4

• x = -4

• x = 8

What indicates that a quadratic equation has no real solutions when graphed?

• The graph does not touch the x-axis

• The graph touches the x-axis once

• The graph touches the x-axis twice

• The graph is a straight line

How can the line of symmetry help in graphing a quadratic equation?

• All of the above

• It indicates equal values on both sides of the graph

• It helps in finding the vertex of the parabola

• It shows where the maximum value occurs

What is the vertex form of a quadratic equation?

• ax^2 + bx + c

• a(x - h)^2 + k

• x = ay^2 + by + c

• None of the above