Question

For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: f(x)=9x^2+5x+3

Answer 1

The values of a, b, and c for the given equation are 9, 5, and 3 respectively. The parabola opens upwards since the coefficient a is positive. The y-intercept is (0, 3).

Step-by-step explanation:

The equation f(x) = 9x^2 + 5x + 3 represents a quadratic function. To find the values of a, b, and c, we can compare the given equation to the standard form of a quadratic function, f(x) = ax^2 + bx + c. In this case, a = 9, b = 5, and c = 3.

The direction in which the parabola opens can be determined based on the sign of the coefficient a. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards. Since a = 9, the parabola opens upwards.

The y-intercept represents the value of y when x = 0. To find it, substitute x = 0 into the equation: f(0) = 9(0)^2 + 5(0) + 3 = 3. Therefore, the y-intercept is (0, 3).

Answer 2

A = 9, B = 5, C = 3

the parabola opens upwards

y-intercept = 3

Step-by-step explanation:

Since the equation is f(x)=9x^2+5x+3, you can determine what a, b, and c are by associating it with a quadratics standard form, ax^2+bx+c. The numbers correspond with each letter in the skeletal equation.

To determine whether the parabola opens up or down, you can simply look at the a value. If x > 0, the the parabola will open upwards, whereas if x < 0, the parabola will open downwards.

To determine y-intercept, just plug in the value of 0 into x and solve for y.