How do you graph the parabola #y=x^2 + 3x-10# using vertex, intercepts and additional points?
1 Answer
Graph the y-intercept (0,-10), the x-intercepts (-5,0) and (2,0) and the vertex
Explanation:
To find the y-intercept, let x = 0 in the original equation:
So the y-intercept is (0, -10)
To find the x-intercepts, let y=0
Now, factor the expression:
Using the zero product rule, set each bracket equal to zero:
Giving the result
So the x-intercepts are
The vertex is on the line (called the axis of symmetry) that is half-way between the x-intercepts. To find the half-way value, find the midpoint between the x-intercepts:
So the axis of symmetry is
Getting common denominators and adding,
Therefore the vertex of the parabola is
Graph the parabola by plotting the vertex, the y-intercept and the x-intercepts and an additional point (-3,-10) which is the matching point to the y-intercept on the other side of the axis of symmetry. These 5 points should give a reasonable representation of the graph of the parabola.