Solving Quadratics by Graphing

What are the roots of the quadratic function y = x² - 2x - 15?

• x = -5 and x = 3

• x = -3 and x = 5

• x = 2 and x = -7

• x = 1 and x = -15

What is the standard form of a quadratic equation?

• y = ax² + bx + c

• y = a(x - h)² + k

• y = mx + b

• y = a(x + b)(x - c)

What is the axis of symmetry in a quadratic function?

• A vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

• A horizontal line that intersects the vertex of the parabola.

• A diagonal line that passes through the origin of the graph.

• A line that represents the maximum or minimum value of the quadratic function.

How do you find the x-intercepts of a quadratic function?

• Set the function equal to zero (y = 0) and solve for x.

• Find the vertex of the parabola.

• Calculate the discriminant of the quadratic equation.

• Evaluate the function at various x-values.

How can you determine the number of real roots of a quadratic function?

• By using the quadratic formula (x = (-b ± √(b² - 4ac)) / 2a)

• By evaluating the function at different points

• By using the discriminant (D = b² - 4ac). If D > 0, there are 2 real roots; D = 0 means 1 real root; D < 0 means no real roots.

• By graphing the function and counting the x-intercepts.

What is the vertex of a quadratic function?

• The point where the graph intersects the x-axis.

• The highest or lowest point on the graph, depending on the direction of the parabola.

• The point where the graph intersects the y-axis.

• The midpoint of the line segment connecting the x-intercepts.

How do you graph a quadratic function?

• Find the vertex, axis of symmetry, x-intercepts, and y-intercept, then plot these points and draw a smooth curve.

• Only plot the vertex and draw a straight line through it.

• Identify the roots and plot them without considering the vertex.

• Draw a horizontal line at the y-intercept and connect it to the x-intercepts.

What is the significance of the coefficient 'a' in a quadratic function?

• It determines the width of the parabola.

• It determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

• It affects the position of the vertex of the parabola.

• It indicates the number of x-intercepts of the quadratic function.

What is the factored form of a quadratic equation?

• y = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

• y = ax^2 + bx + c, where a, b, and c are constants.

• y = a(x + r1)(x + r2), where r1 and r2 are the roots of the equation.

• y = a(x - r1)(x + r2), where r1 and r2 are the roots of the equation.

What are the x-intercepts of a graph?

• The points where the graph crosses the y-axis.

• The points where the graph crosses the x-axis, meaning the value of y is 0 at these points.

• The maximum points of the graph.

• The minimum points of the graph.