Question

Y = x2  + 3x - 10 

For the above quadratic equation find: 



a.The y-intercept. 

b.The x-intercepts if possible. 

c.The vertex. 

d. The line of symmetry.

Answer 1

The y-intercept of the quadratic equation y = x^2 + 3x - 10 is (0, -10). The x-intercepts are the roots of the equation obtained by solving for x when y = 0. The vertex of the equation is at (-1.5, -12.25), and the line of symmetry is the vertical line x = -1.5.

Step-by-step explanation:

To find various components of the quadratic equation y = x2 + 3x - 10, we analyze its structure:

• a. The y-intercept is the value of y when x equals 0. In this equation, if you set x to 0, y will be -10. Hence, the y-intercept is (0, -10).
• b. The x-intercepts are the points where the graph of the equation crosses the x-axis, which occur when y equals 0. To find them, we set the equation to 0 and solve for x: 0 = x2 + 3x - 10. Factoring the quadratic or using the quadratic formula would give us the x-intercepts.
• c. The vertex of a quadratic equation in the form y = ax2 + bx + c can be found by using the formula -b/(2a) for the x-coordinate, and then substituting this back into the equation for y. For our equation, the vertex is at x = -3/2 = -1.5, and y = (-1.5)2 + 3(-1.5) - 10 = -12.25, resulting in the vertex (-1.5, -12.25).
• d. The line of symmetry is a vertical line that passes through the vertex. Since the vertex has an x-coordinate of -1.5, the line of symmetry is x = -1.5.

Answer 2

Note: y = x2 + 3x - 10 should be y = x^2 + 3x - 10, where " ^ " indicates exponentiation.

To find the y-int.: Let x = 0 and find y. That intercept is (0, -10).
To find the x-int.: Set y = x^2 + 3x - 10 = to 0, and solve for x. You could, for example, use the quadratic formula, completing the square, graphing, factoring, etc. x^2 + 3x - 10 = 0 can be factored easily:

(x+5)(x-2)=0, so that x = -5 and x=2. The x-int. are (-5,0) and (2,0).

The x-coord. of the vertex can be found by using the formula x = -b/(2a).
Once you have that, subst. that result into the given formula and calculate y.

The line of symm. has precisely the same form: x = -b/(2a), where
b=3 and a = 1. Here we don't need or care about c= -10.