Step-by-step explanation:
PART A
x-intercept happens when the graph pass through x-axis or when the coordinate y is equal to zero.
5x² + 2x - 3 = f(x)
5x² + 2x - 3 = y
5x² + 2x - 3 = 0
factorize
5x² + 2x - 3 = 0
(5x - 3)(x + 1) = 0
x = 3/5 or x = -1
There are two x-intercepts, those are 3/5 and -1
PART B
When the coefficient of x² is positive, the parabola has minimum vertex.
When the coefficient of x² is negative, the parabola has maximum vertex.
The coefficient of x² is 5, so the parabola has minimum vertex.
x of vertex =
x = -b/(2a)
x = -2/(2 × 5)
x = -2/10
x = -0.2
y of vertex
y = 5x² + 2x - 3
y = 5(-0.2)² + 2(-0.2) - 3
y = 0.2 - 0.4 - 3
y = -3.2
The vertex is (-0.2, -3.2)
PART C
First, define the x-intercept.
x = 3/5 = 0.6and
x = -1
Second, define the axis of symmetry
x = -b/(2a)
x = -2/(2 × 5)
x = -2/10
x = -0.2
Third, determine the vertex
The vertex is (-0.2, -3.2)
Put the x-intercept, axis of symmetry, and the vertex on cartesian plane. After that, draw the parabola.
