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

Please help me. by explaining it step by step.

Answer 1

y intercept is the value without the variable

Answer 2

This is because the y axis is at x=0

Answer 3

So we can find this by plugging in zero:
y = x^2 + 3x - 10
y = (0)^2 + 3(0) - 10
y = -10
This is our y intercept

Answer 4

You can use the quadratic equation to find the zeros of your parabola.

Answer 5

This is the quadratic equation \[\frac{ -b +/-\sqrt(b^2-4ac) }{ 2a }\]
This is the form the parabola has come in :\[ax^2 + bx + c \]

Answer 6

The vertex can be found by converting ax^2 + bx + c into a(x - h)^2 + k. You will need to complete the square to do this.

Answer 7

Your vertex will be (h, k)

Answer 8

Your line of symmetry will be k. We know it will not be h because this parabola is vertical. It would be horizontal if y was squared in our given equation.

Answer 9

so the x-intercepts are? i'm confused on that @swagmaster47

Answer 10

wow... that seems complicated...

here is an easy method

(a) y- intercept substitute x = 0 and then solve to y... that will be the intercept

(b) x - intercepts... set y = 0 then solve

\[x^2 + 3x - 10 = 0\]

this factors... find 2 numbers that multiply to -10 and add to 3, the larger factor is negative and the smaller is positive. this will help you to find the x- intercepts.


(d) the line of symmetry is half way between the x - intercepts... so add the 2 intercepts and have them

(c) substitute the line of symmetry value into the equation and the y- value you get along with the x value for line of x symmetry form the vertex

hope it helps

Answer 11

oops larger factor is positive and the smaller is negative in (b)