For each quadratic, state the direction of opening and the y-intercept
y=x^2 -7x
the sign of the x^2 coefficient determines the opening direction.
set x=0 to find the y-intercept.
you can always type in your function at wolframalpha.com to confirm your results.
thanks oobleck !!!
To determine the direction of opening and the y-intercept for the quadratic equation y = x^2 - 7x, we can observe the equation in the standard form: y = ax^2 + bx + c.
In this case:
a = coefficient of x^2 = 1
b = coefficient of x = -7
c = constant term = 0
1. Direction of Opening:
The coefficient of x^2 (a) determines the direction of opening for a quadratic equation. If a is positive, the parabola opens upwards; if a is negative, the parabola opens downwards.
In this quadratic equation, a = 1, which means the coefficient of x^2 is positive. Therefore, the parabola opens upwards.
2. Y-Intercept:
The y-intercept is the point where the graph of the quadratic equation intersects the y-axis. To find the y-intercept, substitute x = 0 into the equation and solve for y.
Substituting x = 0 in the equation y = x^2 - 7x:
y = (0)^2 - 7(0)
y = 0 - 0
y = 0
So, the y-intercept for the quadratic equation y = x^2 - 7x is (0, 0).