Question

1. the graph of a quadratic function is called a

the parent function is
the a-coefficient tells you if the graph opens
the c-term tells you the

Explanation:

1. The graph of a quadratic function is called a parabola. This is a fundamental concept in the study of quadratic functions (which are of the form \( y = ax^2 + bx + c \)) in Algebra (a subfield of Mathematics). The parabola is the U - shaped (or inverted U - shaped) graph associated with quadratic equations.
2. The parent function of a quadratic function is \( y=x^{2} \). The parent function is the simplest form of a function in a family of functions. For quadratic functions, the basic form without any transformations (like shifts, stretches, or compressions) is \( y = x^{2} \), which has a vertex at the origin \((0,0)\) and opens upwards.
3. The \( a \) - coefficient in the quadratic function \( y = ax^{2}+bx + c \) tells you if the graph opens up or down. If \( a>0 \), the parabola opens upwards, and if \( a < 0 \), the parabola opens downwards. Also, the magnitude of \( |a| \) affects the width of the parabola (a larger \( |a| \) makes it narrower, a smaller \( |a| \) makes it wider), but the sign of \( a \) determines the direction of opening.
4. The \( c \) - term in the quadratic function \( y=ax^{2}+bx + c \) tells you the y - intercept of the graph. When \( x = 0 \), \( y=c \), so the point \((0,c)\) is where the graph intersects the y - axis.

Answer:

1. parabola
2. \( y = x^{2} \)
3. up or down (and affects width)
4. y - intercept