Illustrative Math Quadratics

What is the general form of a quadratic function?

• f(x) = a + bx + c

• f(x) = ax^2 + b

• f(x) = ax^2 + bx + c

• f(x) = ax^3 + bx + c

How can you determine the vertex of a quadratic function from its standard form?

• Use the formula x = -b / (2a) to find the x-coordinate of the vertex, then substitute it back into the function to find the y-coordinate.

• Substitute random values for x and y

• Take the square root of the coefficient of x

• Divide the coefficient of x by the constant term

Explain the concept of maximum or minimum value in relation to quadratic functions.

• The maximum value is always positive

• The maximum or minimum value in relation to quadratic functions is the highest or lowest point on the graph, respectively, determined by the vertex of the parabola.

• The maximum value is the x-intercept of the quadratic function

• The minimum value is the y-intercept of the quadratic function

How can you determine the direction of opening of a parabola based on the coefficient of x^2 in a quadratic function?

• The direction of opening is determined by the coefficient of x^3

• The direction of opening is always upwards regardless of the coefficient of x^2

• The direction of opening is determined by the constant term in the quadratic function

• The direction of opening of a parabola can be determined based on whether the coefficient of x^2 is positive or negative.

Tags

CCSS.HSF-IF.C.7A

Explain how to graph a quadratic function in vertex form.

• When graphing a quadratic function in vertex form, the axis of symmetry is not relevant.

• Graphing a quadratic function in vertex form involves plotting the vertex, finding additional points using symmetry, and connecting the points to form a parabola.

• To graph a quadratic function in vertex form, you only need to plot the vertex and draw a straight line.

• Graphing a quadratic function in vertex form involves plotting the y-intercept and connecting the points to form a parabola.

Tags

CCSS.HSF-IF.C.7A

What is the axis of symmetry of a quadratic function?

• x = -b / (2a) * 2

• x = -b / (2a) + 1

• x = -b / (2a)

• x = -b / (2a) - 1

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

• Divide the y-intercept by the slope of the function.

• Substitute the x-value of the vertex into the function.

• Set the quadratic function equal to zero and solve for x.

• Find the vertex of the parabola.

Tags

CCSS.HSF-IF.C.7A

How does the sign of the leading coefficient of a quadratic function affect its graph?

• If the leading coefficient is positive, the graph opens to the right.

• A negative leading coefficient means the graph is a straight line.

• If the leading coefficient is positive, the graph opens upwards.

• A negative leading coefficient causes the graph to open downwards.

Tags

CCSS.HSF-IF.C.7A

What is the effect of the coefficient 'a' in a quadratic function's equation on the width of its graph's parabola?

• A larger absolute value of 'a' makes the parabola wider, while a smaller absolute value makes it narrower.

• The coefficient 'a' has no effect on the width of the parabola; it only affects the direction in which it opens.

• A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.

• The coefficient 'a' determines the color of the parabola, not its width.

Determine the VERTEX when given the equation

y = (x+7)(x-3)