Question

51. . For any quadraticpolynomial ax^2 + bx + c, a + 0, the graph of the
corresponding equation y = ax^2 + bx + c has shape open up wards parabola like
"U" then the value of a will be a
number

Answer 1

Step-by-step explanation:

Parabolas

The graph of a quadratic equation in two variables (y = ax2 + bx + c ) is called ... If a > 0 ( positive) then the parabola opens upward. ... So the y-intercept of any parabola is always at (0,c)

Answer 2

The value of a will be a positive number.

Given:

The quadratic polynomial y = ax^2 + bx + c

The graph of the equation is in the shape of an upward "U" parabola.

To find:

The value of a

Solution:

• A quadratic polynomial is a mathematical expression that can be written in the form ax^2 + bx + c, where x is a variable, and a, b and c are constants.
• When this expression is graphed on a coordinate plane, it produces a parabola, which is a type of U-shaped curve. The shape of the parabola depends on the value of the constant a.
• If a is positive, the parabola will open upwards, like a "U" shape. This means that the highest point on the curve, known as the vertex, will be the point where the parabola changes direction and begins to curve downwards. This is also the point where the value of the expression ax^2 + bx + c is at its maximum.
• On the other hand, if a is negative, the parabola will open downwards, like an upside-down "U" shape. In this case, the vertex will be the point where the parabola changes direction and begins to curve upwards. This is also the point where the value of the expression ax^2 + bx + c is at its minimum.
• So, if the graph of the equation y = ax^2 + bx + c has the shape of an upwards-opening parabola, like a "U" shape, the value of the constant a will be a positive number.
• This is because a positive value of a will cause the parabola to open upwards and produce the desired shape.

Hence, the value of a will be a positive number.

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