Quadratics Standard Form

Front

Back

down

Answer explanation

The graph of the quadratic function opens down because the coefficient of the x² term is negative (-3). Therefore, the correct answer is 'down'.

Front

Back

(0, 9)

Answer explanation

To find the y-intercept, set x=0 in the equation x^2-3x+9. This gives y=0^2-3(0)+9=9. Thus, the y-intercept is (0, 9), which is the correct choice.

Front

What do we call the graph of a quadratic?

Back

parabola

Answer explanation

The graph of a quadratic function is called a parabola. It has a U-shaped curve, which can open upwards or downwards, distinguishing it from other shapes like lines or vertices.

Front

Does this parabola have a maximum or minimum?

Back

Minimum

Answer explanation

A parabola opens upwards when the coefficient of the x² term is positive, indicating it has a minimum point. Therefore, this parabola has a minimum.

Front

Identify a, b, and c if y = +3x² +5x - 8

Back

a=3, b=5, c= - 8

Answer explanation

In the equation y = +3x² + 5x - 8, the coefficients correspond to a, b, and c. Here, a = 3, b = 5, and c = -8, making the correct choice a=3, b=5, c=-8.

Front

If a is negative in the quadratic function, which way does the parabola open?

Back

down

Answer explanation

In a quadratic function, if the coefficient 'a' is negative, the parabola opens downwards. This means the correct answer is 'down', as the graph will have a maximum point and extend downwards on both sides.

Front

What is the standard form of a quadratic function?

Back

y = ax² + bx + c

Answer explanation

The standard form of a quadratic function is represented as y = ax² + bx + c, where a, b, and c are constants. This form clearly shows the quadratic nature of the function, distinguishing it from other forms listed.

Front

What is the green dot on the parabola called? Options: maximum, minimum, roots, zeros

Back

maximum

Answer explanation

The green dot on the parabola represents the maximum point, where the value of the function reaches its highest point. In contrast, a minimum would be the lowest point, while roots and zeros refer to the x-intercepts.

Front

What do we call the highest or lowest point of a quadratic?

Back

vertex

Answer explanation

The highest or lowest point of a quadratic function is called the vertex. It represents the maximum or minimum value of the function, distinguishing it from other terms like parabola, graph, or point.

Front

What is the y-intercept of the function f(x) = -2x² + 4x - 6?

Back

(0, -6)

Answer explanation

To find the y-intercept, set x = 0 in f(x). f(0) = -2(0)^2 + 4(0) - 6 = -6. Thus, the y-intercept is (0, -6), which corresponds to the correct answer.